Question

an object of size 7 cm is places at 27cm inform of a concave mirror of focal length 18 cm .at what distance from the mirror should the screen be placed,so that a sharp focussed image can be obtained? find the size and nature of image.

Answer 1

Object distance (u)= -27cm
Object height= 7cm
Let image distance be v cm
We know by mirror formula that
1/v + 1/u = 1/f
1/v + 1/(-27) = 1/(-18)
1/v = 1/(-18) + 1/27
1/v= (-3+2)/54
1/v= -1/54
v= -54 cm
Thus, placing a screen at a distance of 54 cm from the concave mirror on the same side as object will give us a sharp and focused image.
The magnification will be
m= -v/u
m= -(-54)/(-27)
m= -2
|m|>1 => enlarged image and the negative sign implies that the image is inverted
m can also be written as
m= Height of image/ Height of object
-2= Height of image/7
Height of image= -14cm
Thus the image has a height of 14 cm and is inverted and present at a distance of 54 cm from the mirror.

Answer 2

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