What Is The Focal Length Of A Makeup Mirror That Has A Power Of 2.35 D?

2.1 Images Formed by Plane Mirrors

26 .

Consider a pair of flat mirrors that are positioned so that they form an angle of 120 $°$ . An object is placed on the bisector between the mirrors. Construct a ray diagram as in Effigy 2.4 to show how many images are formed.

27.

Consider a pair of flat mirrors that are positioned so that they form an angle of 60 $°$ . An object is placed on the bisector betwixt the mirrors. Construct a ray diagram as in Figure 2.4 to show how many images are formed.

28 .

By using more than one flat mirror, construct a ray diagram showing how to create an inverted paradigm.

2.2 Spherical Mirrors

29.

The following figure shows a light seedling between two spherical mirrors. One mirror produces a beam of light with parallel rays; the other keeps calorie-free from escaping without being put into the beam. Where is the filament of the light in relation to the focal betoken or radius of curvature of each mirror?

A light bulb is shown in the centre, with a small concave mirror to its left and a bigger one to its right. The light rays originating from the bulb that hit the smaller mirror are reflected back to the bulb. Light rays from the bulb that hit the bigger mirror are reflected. These reflected rays are parallel and travel towards the left.

30 .

Why are diverging mirrors often used for rearview mirrors in vehicles? What is the main disadvantage of using such a mirror compared with a flat one?

31.

Some telephoto cameras employ a mirror rather than a lens. What radius of curvature mirror is needed to replace a 800 mm-focal length telephoto lens?

32 .

Calculate the focal length of a mirror formed by the shiny dorsum of a spoon that has a three.00 cm radius of curvature.

33.

Electric room heaters utilize a concave mirror to reflect infrared (IR) radiation from hot coils. Note that IR radiation follows the same law of reflection equally visible light. Given that the mirror has a radius of curvature of fifty.0 cm and produces an image of the coils 3.00 m abroad from the mirror, where are the coils?

34 .

Find the magnification of the heater element in the previous problem. Note that its large magnitude helps spread out the reflected energy.

35.

What is the focal length of a makeup mirror that produces a magnification of i.50 when a person's face up is 12.0 cm away? Explicitly testify how you follow the steps in the Spherical Mirrors.

36 .

A shopper continuing three.00 chiliad from a convex security mirror sees his prototype with a magnification of 0.250. (a) Where is his epitome? (b) What is the focal length of the mirror? (c) What is its radius of curvature?

37.

An object 1.50 cm loftier is held three.00 cm from a person's cornea, and its reflected prototype is measured to be 0.167 cm loftier. (a) What is the magnification? (b) Where is the image? (c) Find the radius of curvature of the convex mirror formed past the cornea. (Annotation that this technique is used by optometrists to measure out the curvature of the cornea for contact lens fitting. The instrument used is called a keratometer, or bend measurer.)

38 .

Ray tracing for a flat mirror shows that the image is located a distance behind the mirror equal to the altitude of the object from the mirror. This is stated every bit $d_{i} = − d_{o}$ , since this is a negative image distance (information technology is a virtual epitome). What is the focal length of a flat mirror?

39.

Prove that, for a flat mirror, $h_{i} = h_{o}$ , given that the image is the same distance behind the mirror every bit the distance of the object from the mirror.

xl .

Use the constabulary of reflection to prove that the focal length of a mirror is half its radius of curvature. That is, prove that $f = R / 2$ . Notation this is true for a spherical mirror just if its diameter is small compared with its radius of curvature.

41.

Referring to the electric room heater considered in problem 5, calculate the intensity of IR radiation in ${W/m}^{2}$ projected by the concave mirror on a person 3.00 m away. Assume that the heating element radiates 1500 Due west and has an area of $100 {cm}^{ii}$ , and that half of the radiated power is reflected and focused by the mirror.

42 .

2 mirrors are inclined at an angle of 60 $°$ and an object is placed at a bespeak that is equidistant from the 2 mirrors. Use a protractor to draw rays accurately and locate all images. You may accept to draw several figures so that that rays for different images practise not clutter your cartoon.

43.

Two parallel mirrors are facing each other and are separated by a distance of 3 cm. A point object is placed betwixt the mirrors 1 cm from i of the mirrors. Find the coordinates of all the images.

2.3 Images Formed by Refraction

44 .

An object is located in air xxx cm from the vertex of a concave surface made of glass with a radius of curvature 10 cm. Where does the image by refraction class and what is its magnification? Apply $n_{air} = 1$ and $n_{drinking glass} = 1.5$ .

45.

An object is located in air 30 cm from the vertex of a convex surface made of glass with a radius of curvature lxxx cm. Where does the prototype by refraction course and what is its magnification?

46 .

An object is located in h2o fifteen cm from the vertex of a concave surface made of glass with a radius of curvature 10 cm. Where does the image by refraction course and what is its magnification? Use $n_{water} = 4 / 3$ and ${north}_{drinking glass} = i.five$ .

47.

An object is located in water 30 cm from the vertex of a convex surface made of Plexiglas with a radius of curvature of fourscore cm. Where does the image form by refraction and what is its magnification? $n_{water} = four / 3$ and $n_{Plexiglas} = 1.65$ .

48 .

An object is located in air v cm from the vertex of a concave surface made of glass with a radius of curvature xx cm. Where does the image form by refraction and what is its magnification? Apply $n_{air} = i$ and ${northward}_{glass} = i.5$ .

49.

Derive the spherical interface equation for refraction at a concave surface. (Hint: Follow the derivation in the text for the convex surface.)

2.4 Thin Lenses

50 .

How far from the lens must the motion-picture show in a photographic camera be, if the lens has a 35.0-mm focal length and is being used to photograph a flower 75.0 cm away? Explicitly show how you lot follow the steps in the Lenses.

51.

A certain slide projector has a 100 mm-focal length lens. (a) How far away is the screen if a slide is placed 103 mm from the lens and produces a sharp prototype? (b) If the slide is 24.0 by 36.0 mm, what are the dimensions of the prototype? Explicitly show how yous follow the steps in the Lenses.

52 .

A doctor examines a mole with a 15.0-cm focal length magnifying drinking glass held 13.v cm from the mole. (a) Where is the image? (b) What is its magnification? (c) How big is the image of a 5.00 mm diameter mole?

53.

A photographic camera with a 50.0-mm focal length lens is being used to photograph a person standing 3.00 m abroad. (a) How far from the lens must the pic be? (b) If the film is 36.0 mm high, what fraction of a one.75-m-alpine person will fit on information technology? (c) Discuss how reasonable this seems, based on your experience in taking or posing for photographs.

54 .

A camera lens used for taking shut-up photographs has a focal length of 22.0 mm. The uttermost it tin be placed from the pic is 33.0 mm. (a) What is the closest object that tin exist photographed? (b) What is the magnification of this closest object?

55.

Suppose your 50.0 mm-focal length camera lens is 51.0 mm abroad from the motion-picture show in the camera. (a) How far away is an object that is in focus? (b) What is the summit of the object if its image is two.00 cm high?

56 .

What is the focal length of a magnifying glass that produces a magnification of iii.00 when held five.00 cm from an object, such equally a rare coin?

57.

The magnification of a volume held 7.50 cm from a ten.0 cm-focal length lens is 4.00. (a) Find the magnification for the volume when information technology is held 8.50 cm from the magnifier. (b) Echo for the book held 9.50 cm from the magnifier. (c) Comment on how magnification changes as the object distance increases as in these ii calculations.

58 .

Suppose a 200 mm-focal length telephoto lens is existence used to photo mountains 10.0 km abroad. (a) Where is the epitome? (b) What is the height of the image of a thousand one thousand high cliff on one of the mountains?

59.

A camera with a 100 mm-focal length lens is used to photograph the sun. What is the pinnacle of the epitome of the lord's day on the picture show, given the sun is $1.twoscore \times 10^{6} km$ in diameter and is $1.l \times {ten}^{8} km$ away?

60 .

Use the thin-lens equation to evidence that the magnification for a thin lens is adamant by its focal length and the object altitude and is given by $yard = f / (f - d_{o})$ .

61.

An object of height 3.0 cm is placed v.0 cm in front of a converging lens of focal length twenty cm and observed from the other side. Where and how large is the image?

62 .

An object of top 3.0 cm is placed at 5.0 cm in forepart of a diverging lens of focal length 20 cm and observed from the other side. Where and how large is the image?

63.

An object of height 3.0 cm is placed at 25 cm in front of a diverging lens of focal length 20 cm. Backside the diverging lens, in that location is a converging lens of focal length 20 cm. The distance between the lenses is 5.0 cm. Find the location and size of the last image.

64 .

Ii convex lenses of focal lengths 20 cm and x cm are placed 30 cm autonomously, with the lens with the longer focal length on the right. An object of height 2.0 cm is placed midway between them and observed through each lens from the left and from the correct. Describe what you will see, such every bit where the image(s) will appear, whether they will exist upright or inverted and their magnifications.

two.five The Eye

Unless otherwise stated, the lens-to-retina distance is 2.00 cm.

65.

What is the ability of the eye when viewing an object 50.0 cm abroad?

66 .

Summate the power of the eye when viewing an object 3.00 yard away.

67.

The print in many books averages iii.50 mm in summit. How high is the epitome of the impress on the retina when the book is held 30.0 cm from the eye?

68 .

Suppose a certain person'due south visual acuity is such that he can run across objects clearly that form an paradigm $4.00 μm$ loftier on his retina. What is the maximum distance at which he can read the 75.0-cm-high letters on the side of an airplane?

69.

People who practise very detailed work shut upwards, such as jewelers, often can see objects clearly at much closer distance than the normal 25 cm. (a) What is the power of the eyes of a adult female who can run into an object clearly at a distance of but viii.00 cm? (b) What is the epitome size of a 1.00-mm object, such equally lettering inside a ring, held at this distance? (c) What would the size of the image be if the object were held at the normal 25.0 cm altitude?

seventy .

What is the far betoken of a person whose optics have a relaxed power of 50.5 D?

71.

What is the nigh betoken of a person whose eyes have an accommodated power of 53.v D?

72 .

(a) A laser reshaping the cornea of a myopic patient reduces the power of his middle by ix.00 D, with a $\pm v.0 %$ uncertainty in the last correction. What is the range of diopters for eyeglass lenses that this person might need after this procedure? (b) Was the person nearsighted or farsighted before the procedure? How do you know?

73.

The power for normal close vision is 54.0 D. In a vision-correction procedure, the power of a patient's eye is increased by 3.00 D. Assuming that this produces normal close vision, what was the patient's virtually point earlier the procedure?

74 .

For normal distant vision, the center has a power of 50.0 D. What was the previous far point of a patient who had laser vision correction that reduced the ability of her eye past 7.00 D, producing normal distant vision?

75.

The power for normal afar vision is 50.0 D. A severely myopic patient has a far point of 5.00 cm. By how many diopters should the ability of his middle be reduced in laser vision correction to obtain normal distant vision for him?

76 .

A educatee's optics, while reading the blackboard, have a ability of 51.0 D. How far is the board from his optics?

77.

The power of a doc'south eyes is 53.0 D while examining a patient. How far from her optics is the object that is existence examined?

78 .

The normal power for afar vision is 50.0 D. A young adult female with normal distant vision has a 10.0% power to accommodate (that is, increment) the ability of her optics. What is the closest object she tin meet clearly?

79.

The far point of a myopic ambassador is 50.0 cm. (a) What is the relaxed ability of his eyes? (b) If he has the normal 8.00% ability to accommodate, what is the closest object he can see clearly?

fourscore .

A very myopic man has a far point of 20.0 cm. What power contact lens (when on the eye) volition correct his distant vision?

81.

Echo the previous problem for eyeglasses held one.fifty cm from the eyes.

82 .

A myopic person sees that her contact lens prescription is –iv.00 D. What is her far indicate?

83.

Repeat the previous problem for glasses that are 1.75 cm from the eyes.

84 .

The contact lens prescription for a mildly farsighted person is 0.750 D, and the person has a nigh point of 29.0 cm. What is the power of the tear layer betwixt the cornea and the lens if the correction is ideal, taking the tear layer into account?

2.7 The Uncomplicated Magnifier

85.

If the image formed on the retina subtends an angle of $30 °$ and the object subtends an bending of $5 °$ , what is the magnification of the prototype?

86 .

What is the magnification of a magnifying lens with a focal length of 10 cm if it is held 3.0 cm from the heart and the object is 12 cm from the eye?

87.

How far should you hold a two.1 cm-focal length magnifying drinking glass from an object to obtain a magnification of $10 \times$ ? Assume you place your eye 5.0 cm from the magnifying glass.

88 .

You hold a v.0 cm-focal length magnifying drinking glass equally shut as possible to your centre. If you take a normal most signal, what is the magnification?

89.

You view a mountain with a magnifying glass of focal length $f = x cm$ . What is the magnification?

90 .

You view an object by property a 2.v cm-focal length magnifying drinking glass ten cm away from it. How far from your centre should you concord the magnifying drinking glass to obtain a magnification of $10 \times ?$

91.

A magnifying glass forms an epitome 10 cm on the reverse side of the lens from the object, which is 10 cm abroad. What is the magnification of this lens for a person with a normal near signal if their middle 12 cm from the object?

92 .

An object viewed with the naked eye subtends a $2 °$ bending. If you view the object through a $10 \times$ magnifying glass, what angle is subtended by the paradigm formed on your retina?

93.

For a normal, relaxed eye, a magnifying glass produces an angular magnification of iv.0. What is the largest magnification possible with this magnifying glass?

94 .

What range of magnification is possible with a 7.0 cm-focal length converging lens?

95.

A magnifying drinking glass produces an athwart magnification of four.5 when used by a young person with a near point of 18 cm. What is the maximum angular magnification obtained by an older person with a most point of 45 cm?

2.viii Microscopes and Telescopes

96 .

A microscope with an overall magnification of 800 has an objective that magnifies by 200. (a) What is the angular magnification of the eyepiece? (b) If in that location are two other objectives that tin can be used, having magnifications of 100 and 400, what other total magnifications are possible?

97.

(a) What magnification is produced by a 0.150 cm-focal length microscope objective that is 0.155 cm from the object being viewed? (b) What is the overall magnification if an $viii \times$ eyepiece (one that produces an angular magnification of 8.00) is used?

98 .

Where does an object need to be placed relative to a microscope for its 0.50 cm-focal length objective to produce a magnification of −400?

99.

An amoeba is 0.305 cm away from the 0.300 cm-focal length objective lens of a microscope. (a) Where is the paradigm formed by the objective lens? (b) What is this image's magnification? (c) An eyepiece with a 2.00-cm focal length is placed 20.0 cm from the objective. Where is the final image? (d) What angular magnification is produced by the eyepiece? (e) What is the overall magnification? (See Effigy 2.39.)

100 .

Unreasonable Results Your friends bear witness you an image through a microscope. They tell you that the microscope has an objective with a 0.500-cm focal length and an eyepiece with a v.00-cm focal length. The resulting overall magnification is 250,000. Are these feasible values for a microscope?

Unless otherwise stated, the lens-to-retina altitude is two.00 cm.

101.

What is the angular magnification of a telescope that has a 100 cm-focal length objective and a 2.50 cm-focal length eyepiece?

102 .

Notice the distance between the objective and eyepiece lenses in the telescope in the in a higher place problem needed to produce a final prototype very far from the observer, where vision is almost relaxed. Note that a telescope is commonly used to view very distant objects.

103.

A large reflecting telescope has an objective mirror with a 10.0-m radius of curvature. What athwart magnification does it produce when a 3.00 m-focal length eyepiece is used?

104 .

A small telescope has a concave mirror with a 2.00-thou radius of curvature for its objective. Its eyepiece is a iv.00 cm-focal length lens. (a) What is the telescope's angular magnification? (b) What bending is subtended by a 25,000 km-diameter sunspot? (c) What is the angle of its telescopic image?

105.

A $7.5 \times$ binocular produces an angular magnification of −7.50, acting similar a telescope. (Mirrors are used to brand the image upright.) If the binoculars accept objective lenses with a 75.0-cm focal length, what is the focal length of the eyepiece lenses?

106 .

Construct Your Own Problem Consider a telescope of the type used by Galileo, having a convex objective and a concave eyepiece as illustrated in part (a) of Figure 2.forty. Construct a problem in which you calculate the location and size of the image produced. Among the things to be considered are the focal lengths of the lenses and their relative placements equally well every bit the size and location of the object. Verify that the athwart magnification is greater than one. That is, the bending subtended at the middle past the paradigm is greater than the bending subtended by the object.

107.

Trace rays to find which style the given ray will emerge after refraction through the thin lens in the following figure. Assume thin-lens approximation. (Hint: Pick a betoken P on the given ray in each case. Treat that bespeak as an object. Now, find its prototype Q. Use the rule: All rays on the other side of the lens will either become through Q or appear to be coming from Q.)

Figure a shows a ray not parallel to the optical axis striking a bi-convex lens. Figure a shows a ray not parallel to the optical axis striking a bi-concave lens.

108 .

Copy and draw rays to find the final prototype in the following diagram. (Hint: Detect the intermediate paradigm through lens alone. Use the intermediate image equally the object for the mirror and piece of work with the mirror alone to observe the final prototype.)

Figure shows from left to right: an object with base O on the optical axis and tip P, a bi-convex lens and a concave mirror with center of curvature C. The focal point of the bi-convex on the object side is labeled F subscript 1 and that on the mirror side is labeled F subscript 2.

109.

A concave mirror of radius of curvature 10 cm is placed 30 cm from a thin convex lens of focal length 15 cm. Find the location and magnification of a small seedling sitting fifty cm from the lens by using the algebraic method.

110 .

An object of height 3 cm is placed at 25 cm in forepart of a converging lens of focal length 20 cm. Behind the lens at that place is a concave mirror of focal length 20 cm. The distance betwixt the lens and the mirror is 5 cm. Find the location, orientation and size of the last image.

111.

An object of meridian 3 cm is placed at a altitude of 25 cm in front of a converging lens of focal length twenty cm, to be referred to as the first lens. Backside the lens in that location is another converging lens of focal length 20 cm placed 10 cm from the first lens. There is a concave mirror of focal length 15 cm placed 50 cm from the second lens. Detect the location, orientation, and size of the final image.

112 .

An object of summit 2 cm is placed at 50 cm in front of a converging lens of focal length xl cm. Behind the lens, there is a convex mirror of focal length 15 cm placed xxx cm from the converging lens. Observe the location, orientation, and size of the concluding image.

113.

Two concave mirrors are placed facing each other. One of them has a small hole in the heart. A penny is placed on the lesser mirror (meet the post-obit effigy). When y'all look from the side, a real image of the penny is observed above the hole. Explain how that could happen.

Figure shows the side view of two concave mirrors placed one on top of the other, facing each other. The top one has a small hole in the middle. A penny is placed on the bottom mirror. An image of the penny is shown above the top mirror, just above the hole.

114 .

A lamp of height five cm is placed 40 cm in front of a converging lens of focal length 20 cm. There is a plane mirror 15 cm backside the lens. Where would y'all find the image when y'all await in the mirror?

115.

Parallel rays from a faraway source strike a converging lens of focal length 20 cm at an angle of 15 degrees with the horizontal direction. Find the vertical position of the real epitome observed on a screen in the focal plane.

116 .

Parallel rays from a faraway source strike a diverging lens of focal length 20 cm at an angle of 10 degrees with the horizontal direction. Every bit yous look through the lens, where in the vertical plane the image would appear?

117.

A low-cal bulb is placed 10 cm from a aeroplane mirror, which faces a convex mirror of radius of curvature 8 cm. The plane mirror is located at a distance of 30 cm from the vertex of the convex mirror. Discover the location of two images in the convex mirror. Are at that place other images? If so, where are they located?

118 .

A point source of light is 50 cm in front of a converging lens of focal length 30 cm. A concave mirror with a focal length of twenty cm is placed 25 cm behind the lens. Where does the final image form, and what are its orientation and magnification?

119.

Re-create and trace to discover how a horizontal ray from S comes out after the lens. Use $n_{glass} = 1.v$ for the prism material.

Figure shows two prisms with their bases parallel to each other at an angle of 45 degrees to the horizontal. To the right of this is a bi-convex lens. A ray along the optical axis enters this set up from the left.

120 .

Copy and trace how a horizontal ray from S comes out after the lens. Utilize $due north = one.55$ for the drinking glass.

Figure shows the cross section of a hemisphere to the left and that of a bi-convex lens to the right. A ray along the optical axis enters this setup from the left.

121.

Copy and draw rays to figure out the terminal image.

Figure shows from left to right: an object with base O on the axis and tip P. A bi-concave lens with focal point F1 and F2 on the left and right respectively and a concave mirror with centre of curvature C.

122 .

By ray tracing or by calculation, find the place within the glass where rays from S converge as a effect of refraction through the lens and the convex air-drinking glass interface. Apply a ruler to estimate the radius of curvature.

Figure shows a bi-convex lens on the left and a glass with a convex surface on the right. The lens has focal points F on both sides. The center of curvature of convex glass is C and its radius of curvature is R. Point S is between the lens and its focal point on the left.

123.

A diverging lens has a focal length of xx cm. What is the ability of the lens in diopters?

124 .

Two lenses of focal lengths of $f_{1}$ and $f_{2}$ are glued together with transparent cloth of negligible thickness. Bear witness that the full power of the two lenses simply add.

125.

What volition be the angular magnification of a convex lens with the focal length 2.5 cm?

126 .

What will be the formula for the angular magnification of a convex lens of focal length f if the middle is very close to the lens and the most point is located a distance D from the eye?

Source: https://openstax.org/books/university-physics-volume-3/pages/2-problems

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