Question

(a) With the help of a suitable ray diagram, derive the mirror formula for a concave mirror. 

(b) The near point of a hypermetropic person is 50 cm from the eye. What is the power of the lens required to enable the person to read clearly a book held at 25 cm from the eye?

Answer 1

(a) Mirror Formula: M₁M₂  is a concave mirror having pole P, focus F and centre of curvature C. 

An object AB is placed in front of mirror with point B on the principal axis. The image formed by mirror is A' B' . The perpendicular dropped from point of incidence D on principal axis is DN. 

In ΔABC and ΔA' B'C 

∠ABC = ∠A' B'C  (each equal to 90°) 

∠ACB = ∠A'CB' (opposite angles) 

Both triangles are similar.

Now in ΔDNF and A' B'F

∠DNF = ∠A'B'F (each equal to 90°) 

∠DFN = ∠A'FB' (opposite angles)

∴ Both triangles are similar

If aperture of mirror is very small, the point N will be very near to P, so FN = FP

By sign convention 

Distance of object from mirror PB = -u 

Distance of image from mirror PB' = - v 

Focal length of mirror PF = - f 

Radius of curvature of mirror PC = - R = - 2f 

Substituting these values in (4), we get

The corrective lens must form the image of letters of book placed at 25cm (near point) ofhypermetropic  eye.