Q51P - University Physics with Modern Physics

Question

A thin slit illuminated by light of frequency f produces its first dark band at ±38.2° in air. When the entire apparatus (slit, screen, and space in between) is immersed in an unknown transparent liquid, the slit’s first dark bands occur instead at ±21.6°. Find the refractive index of the liquid.

Step-by-Step Solution

Answer

The refractive index is 1.68

Step 1: Refractive index

If i is the angle of incidence of a ray in a vacuum (the angle between the incoming ray and the perpendicular to the surface of a medium, called the normal), and r is the angle of refraction (the angle between the ray in the medium and the normal), the refractive index n is defined as the ratio of the sine of the angle of incidence to the sine of the angle of refraction;

Step 2: Refractive index of the liquid

Using

Combining it with

In the case of air and m=1;

In the case of liquid;

So, the refractive index is;

Hence, the refractive index is 1.68