Answer to Question #131674 in Optics for Shreesha

Question

Find the refractive index of the material of a prism of angle 59°42', if the angle of minimum deviation produced for a perticular colour of light is 39°28'.
Also find angle of incidence

Answer 1

First convert radians to degrees. Thus:

$59\degree 42= 59+ \frac {42}{60}= 59.7\degree$

$39\degree 42= 39+ \frac {28} {60}=39.46\degree$

$n=\sin \frac {59.7+39.46}{2}= 0.761$

$\sin \frac {59.7} {2}= 0.497$

Thus refractive index we divide the two: $\frac {0.761}{0.497}= 1.53$

$n=1.53$

$\delta_m= 2i-A$

Therefore: $39.46\degree= 2i-59.7\degree$

$i=49.58\degree$