Answer:
(a). The angle of refraction is 19.26°.
(b). That is proved that the rays in air on either side of the glass are parallel to each other
Explanation:
Given that,
Angle of incidence = 30.0°
Index of reflection of glass = 1.52
(a). We need to calculate the angle of refraction for the ray inside the glass
Using snell's law
![\dfrac{\sin i}{\sin r}=\mu](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csin%20i%7D%7B%5Csin%20r%7D%3D%5Cmu)
![\sin r=\dfrac{\sin i}{\mu}](https://tex.z-dn.net/?f=%5Csin%20r%3D%5Cdfrac%7B%5Csin%20i%7D%7B%5Cmu%7D)
Put the value into the formula
![\sin r=\dfrac{\sin 30}{1.52}](https://tex.z-dn.net/?f=%5Csin%20r%3D%5Cdfrac%7B%5Csin%2030%7D%7B1.52%7D)
![r=\sin^{-1}(0.329)](https://tex.z-dn.net/?f=r%3D%5Csin%5E%7B-1%7D%280.329%29)
![r=19.26^{\circ}](https://tex.z-dn.net/?f=r%3D19.26%5E%7B%5Ccirc%7D)
(b). We know that,
The incident ray and emerging ray is equal then the ray will be parallel.
We need to prove that the rays in air on either side of the glass are parallel to each other
Using formula for emerging ray
![\dfrac{\sin e}{\sin r}=\mu](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csin%20e%7D%7B%5Csin%20r%7D%3D%5Cmu)
![\sin e=\sin r\times \mu](https://tex.z-dn.net/?f=%5Csin%20e%3D%5Csin%20r%5Ctimes%20%5Cmu)
Put the value into the formula
![\sin e=0.3289\times 1.52](https://tex.z-dn.net/?f=%5Csin%20e%3D0.3289%5Ctimes%201.52)
![e=\sin^{-1}(0.499)](https://tex.z-dn.net/?f=e%3D%5Csin%5E%7B-1%7D%280.499%29)
![e=29.9\approx 30^{\circ}](https://tex.z-dn.net/?f=e%3D29.9%5Capprox%2030%5E%7B%5Ccirc%7D)
So, ![\sin i=\sin e](https://tex.z-dn.net/?f=%5Csin%20i%3D%5Csin%20e)
This is proved.
Hence, (a). The angle of refraction is 19.26°.
(b). That is proved that the rays in air on either side of the glass are parallel to each other