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Chapter 5: Q7E (page 1105)

A parallel beam of light in air makes an angle of 47.5潞 with the surface of a glass plate having a refractive index of 1.66. (a) What is the angle between the reflected part of the beam and the surface of the glass? (b) What is the angle between the refracted beam and the surface of the glass?

Short Answer

Expert verified
  1. The angle between the reflected part of the beam and the surface of the glass is47.5掳
  2. The angle between the refracted part of the beam and the surface of the glass is胃b=24.0掳

Step by step solution

01

(a) Determination of the angle between the reflected part of the beam and the surface of the glass.

The law of reflection states,

胃i=胃r

Now, refer to the image below,

From, the figure and the law of reflection,

胃a=胃r=42.5掳

Thus, the reflected angle with respect to the glass is,

90.0掳-胃r=47.5掳

02

(b) Determination of the angle between the refracted part of the beam and the surface of the glass.

According to the Snell鈥檚 Law, the reflection, refraction and the normal lie on the same plane and

nasin胃a=nbsin胃b

Therefore,

sin胃b=nasin胃anb=1.00sin42.5掳1.66=0.4070

Thus, the refraction angle with respect to glass is胃b=24.0掳

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