Q: The speed of light in a vacuum is given by Maxwell’s equations. What is its value and which equation relates the speed of light to frequency and wavelength?

$$c = 3.00 \times 10^8$\ \mathrm{m/s}$$ and $$c = f \lambda$$

Q: If the index of refraction of water is $$n = 1.33$$, what is the speed of light in water?

$$v = 2.25 \times 10^8$\ \mathrm{m/s}$$

Q: A ray of light passes from glass ($$n = 1.50) $$into air ($$n = 1.00). $$What is the critical angle for total internal reflection at the glass-air interface?

$$\theta_c = \sin$$^{-1}$$\left(\frac{1.00}{1.50}\right) = 41.8^\circ$$

Q: A light ray travels from medium 1 ($$n_1 = 1.70$) into medium 2 (n_2$ = 1.50$$), and then into medium 3 ($$n_3 = 1.30$). If the ray is incident at the critical angle at the interface between media 2 and 3, what is the value of the critical angle?

$$\theta_c = \sin$$^{-1}$$\left(\frac{1.30}{1.50}\right) = 60.1^\circ$$

Q: A fiber optic cable has a core with $$n_1 = 1.58$ and cladding with n_2$ = 1.53. $$What is the maximum angle $$\theta ($$with respect to the axis) for which light will undergo total internal reflection at the core-cladding boundary?

$$\theta = \sin$$^{-1}$$\left(\frac{1.53}{1.58}\right) = 75.5^\circ$$

Question 1

Which of the following best describes the orientation of the electric field (E), magnetic field (B), and the direction of propagation (c) in an electromagnetic wave traveling in free space?

Accepted Answer

E and B are perpendicular to each other and both are perpendicular to c.

Question 2

The speed of light in a vacuum is given by Maxwell’s equations. What is its value and which equation relates the speed of light to frequency and wavelength?

Accepted Answer

$$c = 3.00 	imes 10^8$\ \mathrm{m/s}$$ and $$c = f \lambda$$

Question 3

A light ray in air (n = 1.00) strikes a glass slab (n = 1.50) at an angle of incidence of $$30^\circ. $$What is the angle of refraction inside the glass? (Use Snell’s Law: $$n_1$$ \sin \$$theta_1$$ = $$n_2$$ \sin \$$theta_2)$$

Accepted Answer

$$\$$theta_2$$ = 19.5^\circ$$

Question 4

Which region of the electromagnetic spectrum has the shortest wavelength?

Accepted Answer

X-rays

Question 5

If the index of refraction of water is $$n = 1.33$$, what is the speed of light in water?

Accepted Answer

$$v = 2.25 	imes 10^8$\ \mathrm{m/s}$$

Question 6

A ray of light passes from glass ($$n = 1.50) $$into air ($$n = 1.00). $$What is the critical angle for total internal reflection at the glass-air interface?

Accepted Answer

$$	heta_c = \sin$$^{-1}$$\left(\frac{1.00}{1.50}ight) = 41.8^\circ$$

Question 7

Which of the following statements about the law of reflection is correct?

Accepted Answer

The angle of incidence equals the angle of reflection, both measured from the normal.

Question 8

A laser emits light with a wavelength of $$780\ \mathrm{nm} in $$air. If the light enters a plastic with $$n = 1.55$$, what is its wavelength in the plastic?

Accepted Answer

$$\lambda = 503\ \mathrm{nm}$$

Question 9

Which phenomenon explains why a prism separates white light into its constituent colors?

Accepted Answer

Dispersion

Question 10

A light ray travels from medium 1 ($$n_1 = 1.70$) into medium 2 (n_2$ = 1.50$$), and then into medium 3 ($$n_3 = 1.30$). If the ray is incident at the critical angle at the interface between media 2 and 3, what is the value of the critical angle?

Accepted Answer

$$	heta_c = \sin$$^{-1}$$\left(\frac{1.30}{1.50}ight) = 60.1^\circ$$

Question 11

Which of the following is true about the frequency and wavelength of light as it passes from air into water?

Accepted Answer

Frequency remains the same, but wavelength decreases.

Question 12

A fiber optic cable has a core with $$n_1 = 1.58$ and cladding with n_2$ = 1.53. $$What is the maximum angle $$	heta ($$with respect to the axis) for which light will undergo total internal reflection at the core-cladding boundary?

Accepted Answer

$$	heta = \sin$$^{-1}$$\left(\frac{1.53}{1.58}ight) = 75.5^\circ$$

Question 13

Which of the following best describes specular reflection?

Accepted Answer

Reflection from a smooth surface, where parallel rays reflect at the same angle.

Question 14

A prism has an apex angle $$\phi = 60^\circ. If $$the angle of incidence $$\$$theta_1$$ = 50^\circ$$ and the angle of emergence $$\$$theta_4$$ = 70^\circ$$, what is the angle of deviation $$\delta$$?

Accepted Answer

$$\delta = 50^\circ + 70^\circ - 60^\circ = 60^\circ$$

Question 15

Which of the following is NOT a property of light rays in the ray model (geometrical optics)?

Accepted Answer

Light rays bend around obstacles due to diffraction.

Question 16

A beam of white light passes through a glass prism. Which color will emerge at the greatest angle of deviation?

Accepted Answer

Violet

Question 17

If a light ray is incident normally (perpendicular) on the interface between two media, what happens to its direction as it passes into the second medium?

Accepted Answer

It continues in the same direction.

Question 18

Which of the following best explains the formation of a rainbow in the atmosphere?

Accepted Answer

Refraction, reflection, and dispersion of sunlight in raindrops.

Question 19

A light ray in air strikes a water surface at $$45^\circ. If $$the refractive index of water is $$n = 1.33$$, what is the angle of refraction in water?

Accepted Answer

$$\$$theta_2$$ = 32.1^\circ$$

Electromagnetic Waves and Geometric Optics: Study Notes

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