Μ1 = 2.42
μ2 = 1.65

refractive index of diamond with respect to flint glass​ is given by : 
μ21 = ​μ1/​μ2 = 2.42/1.65  = 1.46

Introduction:
When a light ray passes from one medium to another, it changes its direction, and the extent of this change depends on the refractive indexes of the two media. In this question, we are given the refractive index of diamond and the refractive index of a liquid, and we need to find the refractive index of diamond with respect to the liquid.

Given:
Refractive index of diamond (n1) = 2.42
Refractive index of liquid (n2) = 1.4

Formula:
The refractive index of diamond with respect to the liquid can be found using the formula:

n1/n2 = sin(i)/sin(r)

where i is the angle of incidence and r is the angle of refraction.

Explanation:
When a light ray passes from one medium to another, it undergoes refraction, which means that it changes its direction. The extent of this change depends on the refractive indexes of the two media. The refractive index of a medium is defined as the ratio of the speed of light in a vacuum to the speed of light in that medium.

In this question, we are given the refractive index of diamond (n1) and the refractive index of a liquid (n2). We can use the formula mentioned above to find the refractive index of diamond with respect to the liquid.

We know that the angle of incidence (i) is the angle between the incident light ray and the normal to the surface of the diamond, and the angle of refraction (r) is the angle between the refracted light ray and the normal to the surface of the diamond.

Solution:
Let us assume that the incident light ray makes an angle of 45 degrees with the normal to the surface of the diamond. We can then use Snell's law to find the angle of refraction:

n1 sin(i) = n2 sin(r)
2.42 sin(45) = 1.4 sin(r)
1.714 = 1.4 sin(r)
sin(r) = 1.714/1.4
sin(r) = 1.224

We can then use the formula mentioned above to find the refractive index of diamond with respect to the liquid:

n1/n2 = sin(i)/sin(r)
n1/n2 = sin(45)/1.224
n1/n2 = 0.707/1.224
n1/n2 = 0.577

Therefore, the refractive index of diamond with respect to the liquid is 0.577.