Chapter 34, Problem 017 More mirrors. Object O stands on the central axis of a s

Question

Chapter 34, Problem 017 More mirrors. Object O stands on the central axis of a spherical or plane mirror. For this situation (The table below. All distances are in centimeters.), find (a) the radius of curvature r (nonzero number or 0 if infinity), (b) the image distance i, (c) the lateral magnification m, whether (d) the image is real or virtual, (e) nverted or noninverted from O, and (f) on the same side of the mirror as object O or on the opposite side Type m R/V I/NI Side Concave 25 (a) Number (b) Number (c) Number Units Units Units

Explanation / Answer

Given

concave mirror with focal length f = 25 cm ,

object distance p = 11 cm

we know the relation between object distance image distance and radius of curvature is  

1/p +1/i = 2/R

and 1/p + 1/i = 1/f ===> R = 2f

so the radius of curvature of the mirror is R = 2*25 = 50 cm

b) image distance is

1/i = 1/f - 1/p

1/i = 1/25 -1/11

i = -19.64 cm

the negative sign indicates that the image is formed on the other side

c) lateral magnification of the mirror is m = -i/p = -(-19.64/11) cm = 1.785455 cm

the image is larger in size than the size of the object

d) the image is virtula image formed by the extended reflected rays in backward direction forming image on other side of the mirror

e) The image is not inverted image it is an erect image

f) image formed on the opposite direction of the mirror

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