Question

An object 4 cm high is placed 40.0 cm in front of a concave mirror of focal length 20 cm. Find the distance from the mirror, at which a screen be placed in order to obtain a sharp image. Also find the size and nature of the image formed. 
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Answer 1

Answer:

An object 4 cm high is placed `40*0` cm in front of a concave mirror of focal length 20 cm. Find the distance from the mirror, at which a screen be placed in order to obtain a sharp image. Also, find the size and nature of the image formed.

check-Solution

Solution :

Here, `h_(1)= 4cm,u= -40cm,f= -20cm,v=?, h_(2)=?`

From `1/u + (1)/(v) =(1)/(f), (1)/(v) = (1)/(f)- 1/u=1/-20 + 1/40 = (-1)/(40)`

or `v= -40 cm`

Therefore, screen should be kept at `40 cm` from the mirror.

From `(h_(2))/(h_(1)) = -v/u, h_(2) = -v/u xx h_(1) = (-(-40))/((-40)) xx 4 = -4 cm`

The image is real, inverted and size `= 4cm`.

Answer 2

Answer:

given that

height of the object(ho)=4cm

object distance (u)=-40cm

focal length (f) =-20cm

we know that

1/v

+1/u =1/f

1/v-1/40=-1/20

1/v=_1/20+1/40

1/v=-1/40

v=-40cm

hence the nature of the image will be real and inverted.

we know that

m=-v/u

m=-(-40)/-40=-1

we know that

m=hi/ho

-1=hi/4

hi=-4cm

hence the size of the image is-4cm