Question

while deriving prism formula , which of the following condition is not satisfied:
a. i = e
b. r1 = r2
c. r = A/2
d. m= i+e+r​

Answer 1

d. m= i+e+r

not satisfied

Answer 2

While deriving the prism formula, the condition m = i + e + r is not satisfied.

In the prism formula,

i = angle of incidence,

e = angle of emergence

For a prism of a small angle, The refracted ray inside the prism becomes parallel to the base by this the angle of incidence becomes equal to the angle of emergence. Therefore, the first condition is satisfied.

r1 = refraction angle at the first face

r2 = angle of incidence on the second face

Due to the properties of optics, when the angle of emergence and angle of incidence is the same then r1 = r2 = r. Therefore, the second condition is also satisfied.

A = angle of the prism

In the prism formula, we know that r1 + r2 = A. So, when r1 = r2 = r then we get 2r = A. Therefore, the third condition is satisfied.