Question

A concave mirror has a focal length of 40 cm determine the object position for which the resulting image will be erect and four times the size of the object

Answer 1

focal length of concave mirror

f = 40cm

according to question height of image is 4 time the height of object so,

let h'= height of image

h= height if object

h'=4h

magnification will be

m = h'/h

m = 4h/h. [ putting value of h']

m= 4

now,

m = -v/u. --(i)

where ,

v = image distance

u = object distance

so, from ( i ) equation we get

4 = -v/u

-4u= v. --( ii )

now, using mirror formula

we get,

1/f = 1/u + 1/v

1/40 = 1/u + 1/(-4u). [from second equation]

1/40 = 1/u - 1/4u

after solving this we get the value of 'u'

which is

u =30cm

Hence the object position is 30cm from the concave mirror.

Answer 2

Answer:

u=30 is the correct answer

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