Section of a refracting surface is shown in Fig. The section is symmetrical about x axis. Refractive index of medium on right of the surface is n with respect to the medium on left of the surface. Parallel monochromatic light rays are incident on the surface as shown in Fig. and the refracted rays are focused at F at a distance f from origin O of the co-ordinate system shown in figure. Calculate equation y(x) of shape of the section shown.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. Since light beam is perpendicular to y-axis and it is focused at F, therefore, number of waves means that number of wavelengths from y-axis to F is same for every ray.
We have to calculate equation of refracting surface, it means we have to obtain a relation between x and y co-ordinates of a point lying on the surface.
Let wavelength of rays in left medium be λ 0 . Then wavelength in right medium will be equal to λ = λ 0 /n.
Now consider two rays as shown in Fig.
(i) a ray along x axis and (ii) a ray through point P (x, y).
Length of path of first ray from y-axis to F = OF = f.
This whole path is traversed by the ray in right medium. Therefore, number of waves in this ray = 
= 
.
Second ray, first, travels a distance x in left medium and then 
distance in right medium. Therefore total number of waves in this ray from y-axis to F
= 
+ 
Since, these two numbers are equal, therefore,
+ 
= 
or (n 2 – 1)x 2 + n 2 y 2 – 2n(n – 1)fx = 0
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems