Question 1

A convex mirror has a radius of curvature $$R = -8.0\ \mathrm{cm}. $$What is the focal length $$f of $$the mirror?

Accepted Answer

$$f = -4.0\ \mathrm{cm}$$

Question 2

Which statement best describes the image formed by a convex mirror for any real object?

Accepted Answer

The image is virtual, upright, and smaller than the object.

Question 3

Santa stands $$0.75\ \mathrm{m}$$ from a shiny ornament with diameter $$7.2\ \mathrm{cm}. If $$Santa's height is $$1.6\ \mathrm{m}$$, what is the approximate height of his image in the ornament?

Accepted Answer

$$3.8\ \mathrm{cm}$$

Question 4

A cylindrical glass rod ($$n = 1.52) $$has a hemispherical end of radius $$2.00\ \mathrm{cm}. An $$object is placed on the axis $$8.00\ \mathrm{cm}$$ from the vertex. What is the image distance $$s'$$ inside the glass?

Accepted Answer

$$s' = +11.3\ \mathrm{cm}$$

Question 5

For a thin lens in air, the lens maker’s equation is:

Accepted Answer

$$\frac{1}{f} = (n-1)\left(\frac{1}{R_1$} - \frac{1}{R_2$}\right)$$

Question 6

A converging lens has a focal length of $$20\ \mathrm{cm}. $$Where will the image be formed if the object is placed $$50\ \mathrm{cm}$$ from the lens?

Accepted Answer

$$s' = 33.3\ \mathrm{cm}$$

Question 7

A diverging lens forms a virtual image that is $$1/3$$ the height of the object and $$20\ \mathrm{cm} in $$front of the lens. Where should the object be placed?

Accepted Answer

$$s = -60\ \mathrm{cm}$$

Question 8

Which aberration is caused by the wavelength dependence of the index of refraction, resulting in different colors focusing at different points?

Accepted Answer

Chromatic aberration

Question 9

A hyperopic (farsighted) eye has a near point at $$100\ \mathrm{cm}. $$What power lens (in diopters) is needed to see objects clearly at $$25\ \mathrm{cm}$$?

Accepted Answer

$$+3.0\ \mathrm{D}$$

Question 10

A myopic (nearsighted) eye has a far point at $$50\ \mathrm{cm}. $$What focal length eyeglass lens is needed to see distant objects clearly, if the lens is $$2\ \mathrm{cm}$$ from the eye?

Accepted Answer

$$-48\ \mathrm{cm}$$

Question 11

Which of the following best describes the function of the lens in the human eye?

Accepted Answer

It changes shape to focus images from objects at different distances onto the retina.

Question 12

What is the formula for lateral magnification $$m$$ for a lens?

Accepted Answer

$$m = -\frac{s'}{s}$$

Question 13

A plano-convex lens is made of glass ($$n = 1.52) $$with $$R_1 = +10$$\ \mathrm{cm}$$, R_2$ = \infty. $$What is its focal length?

Accepted Answer

$$f = +19.2\ \mathrm{cm}$$

Question 14

Which statement about the sign conventions for thin lenses is correct?

Accepted Answer

Object distance $$s is $$positive when the object is on the same side as incoming light.

Question 15

A refracting telescope has an objective lens of focal length $$f_1$$ and an eyepiece of focal length $$f_2. $$What is the angular magnification $$M$$?

Accepted Answer

$$M = \frac{f_1$}{f_2$}$$

Question 16

Which type of lens is used to correct myopia (nearsightedness)?

Accepted Answer

Diverging lens

Question 17

A microscope objective forms a real image $$40\ \mathrm{cm}$$ from the lens. The eyepiece has a focal length of $$5\ \mathrm{cm}. $$What is the angular magnification of the eyepiece if the final image is at infinity?

Accepted Answer

$$M = \frac{25\ \mathrm{cm}}{5\ \mathrm{cm}} = 5$$

Question 18

Which of the following is true about spherical aberration in lenses?

Accepted Answer

It occurs because rays passing through different parts of the lens focus at different points.

Question 19

A camera lens has a focal length $$f$$ and aperture diameter $$D. $$The f-number is defined as:

Accepted Answer

$$f/ D$$

Geometric Optics: Mirrors and Image Formation

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