Question

An object of length 30 cm is placed on principal axis of a concave mirror of focal length 30 cm
un 30 cm Its
one end at a distance of 45 cm as shown. Iflength of image is 10x (in cm) find the value of
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Answer 1

answer : the value of x = 4

given, focal length of concave mirror, f = +30cm

distance between one end of object and mirror, u = +45 cm

using formula, 1/v + 1/u = 1/f

⇒1/v + 1/45 = 1/30

⇒1/v = -1/45 + 1/30

⇒1/v = (-2 + 3)/90 = 1/90

v = 90cm

distance between other end of object and mirror, u' = u + 30cm = 45cm + 30cm = 75cm

using formula, 1/v + 1/u = 1/f

⇒1/v' + 1/75cm = 1/30cm

⇒1/v' = 1/30 - 1/75 = 5/150 - 2/150

⇒1/v' = 3/150

⇒1/v' = 1/50

⇒v' = 50cm

length of image , ∆v = v' - v

= 90 - 50

= 40cm

given, length of image = 10x = 40

⇒x = 4