What is the radius R of a concave spherical mirror at a distance of a = 2 metres from the face of a man if he sees in it his image that is one and a half times greater than on a flat mirror placed at the same distance from the face?
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. On the basis of the formula of a mirror
– 
= 
The linear magnification of the mirror is
= 
According to the initial condition, the angular dimensions of the image on the concave mirror are 1.5 times greater than those on the flat mirror: β = 1.5 α (Fig.)
It is obvious that
tan α = 
and tan β = 
When h << 2a, α and β are small. For small angles
1.5 
.
Upon excluding the unknown quantities 
and b from the equations, we find that f = 
a.
Hence, R = 2f = 3a = 6 metres.
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