UNIT 6 Review - Geometric Optics and Snell's Law

Unit 6 Review

​Equations:

​Be familiar with the sign conventions for mirrors and lenses below and described on the following pages.

- Converging focal lengths are positive.
- Diverging focal lengths are negative.
- Object distances are always positive.
- Real image distances are positive.
- Virtual image distances are negative.
- Inverted image heights are negative.

​Thin Lens and Mirror Equations and Sign Convention

Examples

​Lens and Mirror Image Formation Cases

Fill in the Blank

A convex mirror has a focal length of 20 cm.

What is the object distance if the image distance is −14 cm?

Answer in units of cm. Use 3 significant digits.

.

Fill in the Blank

An object is placed at a distance of 1.5 f from a converging lens of focal length f, as shown.

What is the magnification of the lens? (answer to 2 significant digits)

.

Fill in the Blank

An object is 24.0 cm in front of a concave

mirror. Its real image height is 5.00 times larger

than the object height. What is the radius of curvature of the mirror?

Answer in units of cm with 3 significant digits.

.

​Two Lens Systems

• The image location/height (d_i, h_i) for the first lens becomes the object location/height (d^'_o, h^'_o) for the second lens.

• IF the first image distance is on the VIEWER'S SIDE of the second lens (to the RIGHT OF THE SECOND LENS), THEN the object for the second lens is considered virtual and the second lens object distance should be made a negative value.

• Total magnification is the product of both of the individual lens magnifications.

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Telescope

MICROSCOPES

Fill in the Blank

An object is placed 8 m before a convex lens with focal length 2 m.

Another convex lens is placed 4 m behind the first lens with a focal length 5 m.

Determine the final image location with respect to the second lens. Answer in meters, to 3 significant digits.

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Magnifying Glass

​When considering the magnification of a magnifying glass:

θ is the angle subtended by the object by the unaided eye at the near point of the eye (25 cm).

The maximum magnification occurs when θ' is the angle subtended by the final magnified (virtual) image located at the near point of the eye (d_i = -25cm).

Fill in the Blank

A 15 cm focal length converging lens is used to magnify small newspaper print 0.2 cm high.

Calculate the height of the image for the maximum angular magnification for a normal eye.

Assume the eye focuses at the near point of 25 cm. Answer to 3 significant digits.

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​Total Internal Reflection

Multiple Choice

Light strikes the surface of a prism, n = 1.60,

as shown in the figure.

If the prism is surrounded by a fluid, what is

the maximum index of refraction of the fluid

that will still cause total internal reflection

within the prism?

(Hint: Find the critical angle, or, in other words, find the index of refraction of the fluid, n₂, that results in a refraction angle, θ_2, equal to 90^o using Snell's Law)

• 1.13137

• 1.16474

• 1.05101

• 2.07850

Multiple Choice

A cylindrical cistern, constructed below ground level,

is 3.0 m in diameter and 2.2 m deep and is filled

to the brim with a liquid whose index of refraction is 1.66.

A small object rests on the bottom of the cistern at its center.

How far x from the edge of the cistern can a girl whose

eyes are 1.2 m from the ground stand and still see the object?

Answer in units of m.

• 3.16745 m

• 8.70908 m

• 2.25952 m

• 1.84787 m

• 0.550714 m