Q. 14.5( 128 Votes )

A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?

Answer :

Given,


Size of the candle, h = 2.5 cm


Object distance, u = –27 cm


Image size = h’ = ?


Radius of curvature of the concave mirror,


R = – 36 cm


Now focal length f is given as f = R/2


f = R/2 = -18 cm



The image distance can be obtained using the mirror equation,



Where,


f is the focal length


u is object distance and


v is the image distance





v = -54 cm


Therefore, the screen should be placed at a distance of 54 cm


from the mirror to obtain a sharp image.


The magnification is given by



Where,


m is the magnification


h’ is the height of the image


h is the height of the object


v is the image distance


u is the object distance


Using the equation, we get,




h = -5 cm


The height of the image is 5cm. The negative sign indicate that the image is real, inverted and magnified.



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