Spherical mirrors Object O stands on the central axis of a s

Spherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation object distance is ps = +22 cm, the type of mirror is concave, 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.

Solution

a)

Radius of curvature

R=2f =2*40 =80 cm

b)

from thin lens formula

1/f = 1/p + 1/i

1/40 = 1/22 +1/i

i=-48.9 cm

b)

Magnification

M=-i/p =-(-48.9)/22 =2.22

d)

Image is virtual since image distance is negative

e)

The image is noninverted ,since the Magnification is positive

f)

A virtual image is formed on the opposite side of the mirror from the object.