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These questions may be used to make you own problem sheets.

1. Light travelling through air, strikes a piece of flat glass at an angle of 33°. What angle

will the refracted ray make to the normal line between the air-glass surface? The index of

refraction of the glass is 1.568.

2. Light travelling through glass exits the glass into a body of water. If the refracted ray

makes an angle of 44° with the normal, what was the angle of the incident ray? The index

of refraction of the glass is 1.747 and that of the water is 1.33.

3. Determine the critical angle for light traveling from water (n= 1.33) to air.

An unknown material is sitting in air. Light incident upon the material at an angle of 43°

is bent to a refracted angle of 25°. What is the index of refraction of the unknown


4. The speed of a sound wave is 1320 ms-1 in water and 344 ms-1 in air. a) Which medium

has the higher index of refraction for sound? b) What is the critical angle for a sound

wave incident on the surface between air and water?

5. A ray of light travels though a piece of glass (index of refraction of 1.58) is incident on

an interface with air. What is the largest angle the ray can make with the normal and not

be totally reflected back into the glass?
6. The critical angle for total internal reflection at a liquid- air interface is 36.0°. a) If a

ray of light travelling in the liquid has an angle of incidence at the interface of 28.0°,

what angle does the refracted ray in the air make with the normal? b) If a ray of light

travelling in air has an angle of incidence at the interface of 28.0°, what angle does the

refracted ray in the liquid make with the normal?

7. A point source of light is 32.0 cm below the surface of a lake. Find the diameter of the

largest circle at the surface through which light can emerge from the water. hint..

remember to find the maximum angle that causes light to totally internally reflected

assume water has a refractive index of 1.30.

8. A method for measuring index of refraction. A microscope is focused on the upper

surface of a glass plate. A second plate is then placed over the first. To focus on the

bottom surface of the second plate, the microscope must be raised 0.80 mm. To focus on

the upper surface, it must be raised 2.00 mm farther: Find the index of refraction of the

second plate.

9. Light travelling in water strikes a glass plate at an angle of incidence of 55.0°, part of

the beam is reflected and part is refracted. If the reflected and refracted portions make an

angle of 90.0° with each other, what is the index of refraction of the glass?
10. A ray of light is incident in air on a block of ice whose index of refraction is n = 1.33.

What is the largest angle of incidence  for which total internal reflection will occur at

the vertical face.

11. A ball is embedded below the surface of a sheet of ice. (n = 1.309) the distance from

the top surface of the ball to the top layer of ice is 20cm. What is its apparent depth when

viewed at normal incidence of the object.

Graphical Methods for Lenses

1. A converging lens with a focal length of 20.0 cm forms a l real image 2.00 cm tall,

30.0 cm to the right of the lens. Determine the position and size of the object. Is the

image erect or inverted?

Draw a ray diagram for this situation.

Repeat the previous example for the case in which the lens is diverging with a focal

length of -20.0 cm.

2. A converging lens has a focal length of 30.0 cm. For an object to the left of the lens, at

distances of 40.0 cm and 10.00 cm, determine a) the image position b) the magnification

c) whether the image is real or virtual d) whether the image is erect or inverted. Draw a

ray diagram for each case.
3. Where must you place an object in front of a concave mirror with radius R so that the

image is real and one-third the size of the object? Where is the image?

4. A concave mirror is to form an image of the filament of a headlight lamp on a screen

2.00 m from the mirror. The filament is 2.50 mm tall, and the image is to be 18.0 cm tall.

a) How far in front of the vertex of the mirror should the filament be placed? b) What

should be the radius of curvature of the mirror?

5. A mirror on the passenger side of your car is convex and has a radius of curvature with

magnitude 20.0 cm. Another car is 8.0 m behind you and is seen in this side mirror. If this

car is 1.5 m tall, what is the height of the image? (These mirrors usually have a warning

attached that objects viewed in them are closer than they appear. Why is this so?)

5. Niamh has woken early on Christmas morning and is 24.0 cm from the center of a

silvered spherical glass Christmas tree ornament 8.00 cm in diameter. What are the

position and magnification of her image?

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