Q: An upright object is placed $$25 cm $$from a converging lens with $$f = 50 cm. $$What is the image distance?

$$50$$ \text{ cm}$ (on the same side as the object, virtual image)

Q: A second, identical lens is placed $$10 cm to $$the right of the first lens. For an object at $$25 cm $$from the first lens, what is the final image position relative to the second lens?

$$25$$ \text{ cm}$$ \, (to the right of the second lens)$$

Question 1

A single slit of width $$a = 0.5 mm is $$illuminated by light of wavelength $$\lambda = 600 nm. $$What is the angular separation (in degrees) between the first two minima ($$m=1$$ and $$m=2) of $$the diffraction pattern as measured from the center of the slit?

Accepted Answer

$$0.069^\circ$$

Question 2

Two slits, each with a width of $$0.1 mm$$, are separated by $$0.7 mm $$and illuminated by light with a wavelength of $$400 nm. $$Accounting for diffraction effects, what is the intensity of the light at an angle of $$0.5^\circ$$ from the center, in terms of the peak intensity $$I_0$$?

Accepted Answer

$$0.13 I_0$

Question 3

The James Webb Space Telescope (JWST) has a $$6.5 m $$diameter mirror and is used as a spy satellite at $$407 km $$altitude. At $$\lambda = 600 nm$$, what is the minimum separation between two shiny pennies on the ground so that they can be resolved by the JWST? (Neglect atmospheric effects.)

Accepted Answer

$$4.6$$ 	ext{ cm}$

Question 4

A diffraction grating has $$10,000$$ lines/cm. A red laser ($$\lambda = 700 nm) $$and a green laser ($$\lambda = 500 nm) $$are directed through the grating. For the first order ($$m=1) $$principal maxima, what is the angular separation (in degrees) between the red and green maxima?

Accepted Answer

$$14.4^\circ$$

Question 5

Unpolarized light passes through a stack of polarizers, each oriented $$10^\circ$$ from the previous one. What is the minimum number of polarizers needed so that the output intensity is $$10\% of $$the input intensity ($$0.1 I_0$)?

Accepted Answer

$$54$$

Question 6

A concave spherical mirror has a focal length $$f$$ and radius of curvature $$r$$ where $$f = r/2. If $$the image distance equals the object distance, what are the object and image distances in terms of $$r$$?

Accepted Answer

$$r$$

Question 7

Monochromatic yellow light is incident on an equilateral glass prism ($$n=1.10) at$$ $$30^\circ to $$one face. What is the angle (with respect to the normal) at which the yellow light emerges from the opposite face?

Accepted Answer

$$24.8^\circ$$

Question 8

What property of glass causes white light to be separated into the colors of the rainbow when passing through a prism?

Accepted Answer

Dispersion, because the index of refraction $$n$$ depends on wavelength $$\lambda.$$

Question 9

A converging lens is made from material with $$n=1.4. $$One surface has a radius of curvature $$R_1 = 20$ cm. If the lens is to have a focal length of 50$ cm, what is the radius of curvature R_2$ of the second surface?

Accepted Answer

$$-70$$ 	ext{ cm}$

Question 10

An upright object is placed $$25 cm $$from a converging lens with $$f = 50 cm. $$What is the image distance?

Accepted Answer

$$50$$ 	ext{ cm}$ (on the same side as the object, virtual image)

Question 11

Which combination of terms best describes the image formed by a converging lens when the object is placed between the lens and its focal point?

Accepted Answer

virtual, upright

Question 12

Which eye defect(s) could a converging lens help to correct?

Accepted Answer

presbyopia

Question 13

A second, identical lens is placed $$10 cm to $$the right of the first lens. For an object at $$25 cm $$from the first lens, what is the final image position relative to the second lens?

Accepted Answer

$$25$$ 	ext{ cm}$$ \, (to the right of the second lens)$$

Question 14

Which equation describes the condition for the minima in a single-slit diffraction pattern?

Accepted Answer

$$a \sin 	heta = m \lambda$$

Question 15

A beam of unpolarized light passes through two ideal polarizers. If the angle between their axes is $$60^\circ$$, what fraction of the original intensity is transmitted?

Accepted Answer

$$\frac{1}{2} \cos^2$ 60^\circ$$

Question 16

Which of the following best explains why the sky appears blue?

Accepted Answer

Rayleigh scattering, which is more effective for shorter wavelengths (blue light).

PHY222 Midterm #3 Study Guidance: Diffraction, Optics, and Polarization

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