Question

an object 3 cm high is placed at a distance of 8 cm from a concave mirror which produces a virtual image 4.5 cm high what is the focal length of the mirror what is the position of the image and draw a ray diagram to show the formation of the image

Answer 1

Hey!

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Height of the object (h) = 3 cm
Distance of object from concave mirror (u) = -8 cm
Height of the virtual image formed (h') = 4.5
Let's find 'v' first =

- v/u = h'/h
v = - u × h'/h
v = - ( -8) × 4.5 / 3
v = 12 cm

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(i) Focal length of mirror = ?

1/f = 1/v + 1/u
1/f = 1/12 + 1/ -8
1/f = -1/24
1 × 24 = -f
24 = -f

f = -24 cm

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(ii) Position of image (v) = 12 cm

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(iii) Ray diagram - Refer pic

(Image is vertical , thus erect)

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Hope it helps...!!!

Answer 2

Given,

Object height = 3cm

Object distance = -8cm

Image height = 4.5 cm

M= hi/ho

4.5/3=1.5 cm

1.5 = -v/ u= -(-8)/u

U= 8 x 1.5=12 CM

Focal length of the mirror

1/f= 1/u +1/v

1/f=1/12+1/-8

1/f=2-3/24= -1/24

1/f = -1/24

f/1 = -24