Question

The optical path length followed by ray from point A to B given that laws of reflection are obeyed as shown in the figure is
a. Maximum
b. Minimum
c. Constant
d. None of these

Answer 1

Hint: Here, we will use Fermat’s Principle of Extremum path. Fermat's principle states that “light travels between two points along the path that requires the least time, as compared to other nearby paths.” From Fermat's principle, one can derive (A) the law of reflection [the angle of incidence is equal to the angle of reflection] and (B) the law of refraction [Snell's law].

Complete step by step answer: According to Fermat’s Principle of extremum path, when light travels between two points A and B, it follows that path which requires the least time or minimum time.
Light travels along a path having minimum optical path length. But it is found that there are a number of cases in which the real path of light is the one for which the take taken is not a minimum but maximum.
-In the case of a spherical reflector, light prefers maximum time.
-In the case of an elliptical reflector, the light may take the same time for all paths.
So, the modified Fermat’s principle will be, a light ray traveling from one point to another point will traverse a path for which, compared to all neighboring paths, the time required is minimum or maximum or stationary. Since, in the question, we have a spherical reflector, therefore, the path length traveled by the light will be maximum.
Hence, option (a) is the correct answer.

Note: Fermat’s principle gives us an idea about both time and path length. One needs to be careful while considering the conditions for maximum and minimum path length and time. They are two different things and might affect the answer.