a 5mm high object is 30mm from a convex mirror of 25mm radiu

a 5mm high object is 30mm from a convex mirror of 25mm radius. A concave mirror of equal radius is 50 mm away. Find the position and size of the image after reflection at each mirror.

Solution

For convex mirror

Focal length

f=-R/2 =25/2 =-12.5 mm

From thin lens formula

1/f =1/d_i + 1/d_o

-1/12.5 =1/d_i + 1/30

d_i =- 8.82 mm

Since Magnification

M=-d_i/d_o =h_i/h_o

=>-(-8.82)/30=h_i/5

h_i = 1.47 cm

For Concave mirror

f=R/2 =12.5 m

=>1/12.5 =1/d_i + 1/50

d_i = 16.67 mm

M=-16.67/50 =h_i/5

h_i =-1.67 cm