a A concave spherical mirror forms an inverted image 400 tim

(a) A concave spherical mirror forms an inverted image 4.00 times larger than the object. Assuming the distance between object and image is 0.300 m, find the focal length of the mirror.
m

(b) Suppose the mirror is convex. The distance between the image and the object is the same as in part (a), but the image is 0.500 the size of the object. Determine the focal length of the mirror.
m

Solution

concave spherical mirror

-1/f = 1/v - 1/u

m = 4 => V = 4u

V + u = 0.3

=> V = 4*0.3/5 = 0.24

=> f = -1/(1/0.24 - 5/0.7) = - 0.336 m

convex spherical mirror

1/f = 1/v + 1/u

m = 0.5 => v = 0.5 u

v + u = 0.3

1.5 u = 0.3

=> f = 1/((1/(0.5*0.3/1.5) + (1/(0.3/1.5)) = 0.0666 m