Question

Spherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation object distance is p_s = +24 centimeters, the type of mirror is convex, and then the distance between the focal point and the mirror is 40 cm (without proper sign). Find (a) the radius of curvature r (including sign), (b) the image distance i, and (c) the lateral magnification m. Also, determine whether the image is (d) real or virtual, (e) inverted from object O or noninverted, and (f) on the same side of the mirror as O or on the opposite side.

Answer 1

a] Focal length of the mirror = f = - 40 cm

so, radius of curvature = R = f/2 = - 20 cm

b] Use the equation for mirror,

1/f = 1/i + 1/o

=> - 1/40 = 1/i + 1/24

=> i = - 15 cm

this is the image distance. Since the optical system is a mirror, a negative sign on the image indicates that the image is on the other side of the object.

c] Lateral magnification m = image distance / object distance

=> m = - i/o = 0.625.

d] The image is virtual since the optical system is a mirror.

e] Image is upright and f] Image is on the other side of the object.