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Rina8888 [55]
3 years ago
12

For a certain optical medium the speed of light varies from a low value of 1.90 × 10 8 m/s for violet light to a high value of 2

.00 × 10 8 m/s for red light. (a) Calculate the range of the index of refraction of the material for visible light. (b) A white light is incident on the medium from air, making an angle of 30.0° with the normal. Compare the angles of refraction for violet light and red light. (c) Repeat the previous part when the incident angle is 60.0°.
Physics
1 answer:
Dmitry_Shevchenko [17]3 years ago
6 0

Answer:

a. The refractive index ranges from 1.5 - 1.56

b. 18.7° for violet light and 19.5° for red light.

c. 33.7° for violet light and 35.3° for red light.

Explanation:

a. The refractive index of an object is the ratio of the speed of light in a vacuum and the speed of light in the object.

Mathematically,

n = \frac{c}{v}

The speed of violet light in the object is 1.9 * 10^8 m/s.

The speed of red light in the object is 2 * 10^8 m/s

Hence, the refractive index for violet light is:

n = \frac{3 * 10^8 }{1.9 * 10^8} \\\\n = 1.56

and for red light, it is:

n = \frac{3 * 10^8 }{2 * 10^8} \\\\n = 1.5

Hence, the refractive index ranges from 1.5 - 1.56.

b. The refractive index is also the ratio of the sine of the angle of incidence to the sine of the angle of refraction.

n = \frac{sin(i)}{sin(r)}

The angle of incidence is 30°.

The angle of refraction for violet light will be:

1.56 = \frac{sin(30)}{sin(r)}\\ \\sin(r) = \frac{sin(30)}{1.56}  = \frac{0.5}{1.56} \\\\sin(r) = 0.3205\\\\r = 18.7^o

And the angle of refraction for red light will be:

1.5 = \frac{sin(30)}{sin(r)}\\ \\sin(r) = \frac{sin(30)}{1.5}  = \frac{0.5}{1.5} \\\\sin(r) = 0.3333\\\\r = 19.5^o

The angle of refraction for red light is larger than that of violet light when the angle of incidence is 30°.

c. The angle of incidence is 60°.

The angle of refraction for violet light will be:

1.56 = \frac{sin(60)}{sin(r)}\\ \\sin(r) = \frac{sin(60)}{1.56}  = \frac{0.8660}{1.56} \\\\sin(r) = 0.5551\\\\r = 33.7^o

And the angle of refraction for red light will be:

1.5 = \frac{sin(60)}{sin(r)}\\ \\sin(r) = \frac{sin(60)}{1.5}  = \frac{0.8660}{1.5} \\\\sin(r) = 0.5773\\\\r = 35.3^o

The angle of refraction for red light is still larger than that of violet light when the angle of incidence is 60°.

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