Spherical mirrors. Object O stands on the central axis of a spherical mirror. Fo

Question

Spherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation object distance is ps = +23 centimeters, the type of mirror is convex, and then the distance between the focal point and the mirror is 15 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.

Explanation / Answer

Given

convex mirror of

object distance ps = 23 cm ,

focal length f = 15 cm

we know that the radius of curvature of sherical mirror is  

a)

R = 2*f = 2*15 = 30 cm

and using the relation between the object distance image distance and focal lengrh

1/ps + 1/ps' = 1/f = 2/R

and R is negative for convex mirror  

b) 1/ps' = 1/f-1/ps

1/ps' = -1/15 -1/23

ps' = -9.08 cm

-ve sign indicates that the image is virtual image formed on the other side of the mirror

from sign rules if the image formed is not on the side of the outgoing rays then image distance is -ve.

c)

the lateral magnification is  

m = -ps'/ps = -(-9.08)/23 = 0.395

d) image is virtual image  

e) non inverted from the object O

f) image is on the opposite side of the mirror O

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