Optics Package

Mirrors

1) Determine the image distance and image height for a 5.00cm tall object placed 20.0cm from a concave mirror having a focal length of 15.0cm. [60.cm, -15cm]

2) A convex mirror in an amusement park has a radius of curvature of 2.00m. A man stands in front of the mirror so that his image is half as tall as his actual height. At what distance must the man focus his eyes in order to see his image? [-0.50m]

3) A concave mirror in an amusement park has a radius of curvature of 5.0m. A child stands in front of the mirror so that he appears 3.5 times taller than his actual height. If the image is upright, how far is he standing from the mirror? [1.8m]

4) A woman stands 3.0m in front of a convex mirror and notices that her image height is ¼ her actual height. Determine the radius of curvature of the mirror. [2.0m]

5) A spherical concave mirror has a radius of curvature of 5.0cm. At what distance from the mirror should a 2.5cm object be placed to obtain an image that is 36cm tall? [2.3cm]

6) An object is 2.0m in front of a mirror. A virtual image is formed 15.0m behind the mirror. What is the radius of curvature of the mirror? [4.6m]

7) A 0.135m pencil is oriented perpendicular to the principle axis of a concave spherical mirror that has a radius curvature of 0.400m. What are the image distance and the image height if the pencil is 0.240m from the mirror? [1.2m, -0.68m]

8) A convex mirror has a radius of curvature of 0.30m. Where must an object be placed in front of the mirror such that the image is formed 0.10m behind the mirror? [0.30m]

9) A dime is placed in front of a concave mirror that has a radius of curvature 0.20m. The image of the dime is inverted and three times the size of the object. Determine the distance between the dime and the mirror. [0.13m]

10) The inverted image of a light bulb is formed on a screen located 8.00m from a spherical mirror. The image is 3.00 times larger than the light bulb. Determine the object distance and the type of mirror used. [2.7m, concave]

11) An object 5.0cm tall is placed 7.0cm in front of a concave mirror. If a real image is produced that is also 5.0cm tall but inverted, what is the focal length of the mirror? [3.5cm]

12) A convex mirror produced an image that is 3.0cm behind the mirror. If the focal length of this mirror is 5.0cm, at what distance from the mirror is the object placed? [1.9cm]

13) An object 4.0cm tall is placed 8.0cm in front of a concave mirror. If the real image produced is -6.0cm tall, what is the focal length of the mirror? [4.8cm]

14) A convex mirror has a focal length of -10.8cm. An object is placed 32.7cm from the mirror's surface. Determine the image distance. [-8.1cm]

15) An object 3.0cm tall is placed 6.0cm in front of a mirror. If a virtual image is produced that is 1.0cm tall, what is the focal length of the mirror? What kind of mirror is used? [-3.0cm, convex]

16) A student wishes to place an object in front of a concave mirror in order to produce an image one-half the inverted object’s size. If the focal length of the mirror is 5.0cm, how far from the mirror should the object be placed? [15cm]

17) A convex mirror has a focal length of -12cm. A light bulb with a diameter of 6.0cm is placed 60.0cm in front of the mirror. Determine the image distance. [-10.cm]

18) An object 3.0mm high is 10.0cm in front of a concave mirror having a 6.0cm focal length. Find the magnification and the height of the image. [-1.5, -0.45cm]

19) A concave mirror has a focal length of 9.0cm. A 15mm tall object is placed 6.0cm from the mirror. How high is the image? [4.5cm]

20) An object 3.0cm tall produces a virtual image that is 2.0cm tall. If the image is 2.5cm behind the mirror, what is the focal length of the mirror? What kind of mirror is used? [-7.3cm, convex]

21) A convex mirror is needed to produce an image located 24cm behind the mirror that is three-quarters the size of the object. Determine the focal length. [-96cm]

22) A 4.0cm high candle is placed 10.0cm from a concave mirror having a focal length of 16.0cm. Where is the image located? What is the height of the image? [-27cm, 11cm]

23) Determine the focal length of a convex mirror which produces an image that is 16.0cm behind the mirror when the object is 28.5cm from the mirror. [-36cm]

24) Determine the image distance and image height for a 5.00cm tall object placed 45.0cm from a concave mirror having a focal length of 15.0cm. [23cm, -2.6cm]

Lenses

1) A glowing object 4.0cm tall is placed 6.0cm from a concave lens. If a virtual image is produced that is 2.0cm tall, what is the focal length of the lens? [-6.0cm]

2) An object that is 3.0cm tall is placed 6.0cm in front of a convex lens. If the image produced is 4.5cm tall, what is the focal length of the lens? [18cm]

3) Determine the image distance and image height for a 5.0cm tall object placed 30.0cm from a double convex lens having a focal length of 15.0cm. [30.cm, -5.0cm]

4) A double concave lens has a focal length of -10.8cm. An object is placed 32.7cm from the lens's surface. Determine the image distance. [-8.1cm]

5) An inverted image is magnified by 2 when the object is placed 22cm in front of a double convex lens. Determine the image distance and the focal length of the lens. [44cm, 15cm]

6) Determine the focal length of a double concave lens which produces an image that is 16.0cm behind the lens when the object is 28.5cm from the lens. [-36cm]

Reflection

1) If the angle of incidence of a ray of light to a mirror is 20.0o, what angle does the light ray make with the mirror when it reflects? [20.0o]

2) If a ray of light makes an angle of 58o with a mirror, what is the angle between the incident ray and the reflected ray? [116o]

3) A ray of light strikes a mirror at angle of 53° to the normal. What is the angle of reflection? What is the angle between the incident ray and the reflected ray? [53o, 106o]

4) A ray of light strikes a mirror at an angle of reflection of 28°. What is the angle of incidence? [28o]

5) A ray of light incident upon a mirror makes an angle of 36.0° with the mirror. What is the angle between the incident ray and the reflected ray? [72.0o]

Snell’s Law

1) The speed of light in a clear liquid is 1.195´108 m/s. What is its index of refraction? [2.51]

2) A beam of light passes from amber (n=1.55) into silicon (n=3.96). If the angle in amber is 37°, what is the angle in silicon? [13.6o]

3) What is the index of refraction of a substance if the angle of incidence to this substance is 53.0o in air and the angle of refraction in this substance is 41.0o? [1.22]

4) A ray of light strikes the surface of water (n=1.33) at an angle of 60.0° from the water surface. What is the angle of refraction? [40.6o]

5) Light going from glass (n=1.50) to ethanol has a critical angle of 63°. What is the index of refraction of ethanol? [1.34]

6) A beam of light strikes the surface of a block of glass (n=1.50) and produces a refracted angle of 10.0o. What is the incident angle? [15.1o]

7) What is the critical angle for a glass-air interface if the index of refraction of glass is 1.50? [41.8o]

8) The critical angle for a certain liquid-air interface is 48.8o. What is the index of refraction of the liquid? [1.33]

9) What is the critical angle of a substance whose index of refraction is 1.81? [33.5o]

10) Find the critical angle for total internal reflection for light going from ice (n=1.31) into air. [49.8o]