Question

A ray of light travelling in a transparent medium of refractive
index μ , falls on a surface separating the medium from air at
an angle of incidence of 45°. For which of the following
value of m the ray can undergo total internal reflection?
(a) μ = 1.33 (b) μ = 1.40 (c) μ = 1.50 (d) μ = 1.25

Answer 1

Answer: (c) 1.50

Explanation:

Total internal reflection is the complete reflection of light ray within an optically denser medium. You should know that there are 2 condition for total internal reflection which is 1) The light ray must travel from an optically denser medium to an optically less dense medium and 2) The angle of incidence in the optically denser medium must be greater than the critical angle.The second condition is more applicable to this question as if you notice using snells law $\frac{sin(i)}{sin(r)}$ for all the four refractive index , the r value will also be lesser than  i(angle of incidence), which doesnt fit in the first condition as when light is travelling from an optically denser mediu to a less dense, light will end awya from the normal which means that r>i, which is not the case for the following index. Thus we use the other condition which is applicable to another formula which is $n(refractive index)=\frac{1}{sin(c)}.$ where c is the critical angle. Hence when calculating we must ensure that i>c(anything less than 45). Through trial and error, the answer is 1.50 as

$c=sin^{-1} (\frac{1}{1.50} )=41.8$ and this fits in that 45>41.8. Thus, it fits the second condition and hence can undergo total internal reflection. Btw the rest of the refractive index gives the critical angle a value more than 45 which doesn't meet the condition. Hence the answer is (c)=1.50