Question

If p. q, r denote the object distance, image distance and the radius of curvature respectively of a spherical mirror, then prove that r= 2pq/(p+q).

Answer 1

r = 2pq / (p + q)

Given:

p. q, r denotes the object distance, image distance and the radius of curvature respectively of a spherical mirror

To prove:

r= 2pq/(p+q)

Solution:

Using the formula for spherical mirrors,

(1 / f) = (1 / u) + (1 / v)

Here,

u = p

v = q

f = r/2

Substituting these values in the formula, we get

(1/(r/2)) = (1/p) + (1/q)

=> 2/r = (1/p) + (1/q)

=> 2/r = (q + p)/pq

=> 2/r = (p + q)/pq

=> 1/r = (p + q)/2pq

Reciprocating this equation, we get

=> r= 2pq/(p + q)

Hence, proved that r = 2pq / (p + q)

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