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?

Explanation

Here, object hight `h_1` = 2.5 cm for concave mirror,
Object distance u = -27 cm
Radius of curvature R = -36 cm
Focal lenght f = -18 cm
From mirror equatoin,
`1/f = 1/u + 1/v`
`therefore 1/v= 1/f = 1/u = 1/(-18) - 1/(-27) = (-1)/18 + 1/(27)`
`therefore 1/v = (-3 + 2)/(54) = -1/54`
Thus,image will be obtained at -54 c from mirror .
`rArr` Magnification
` m = -v/u`
`therefore h_2/h_1 = -(-54)/(-27)`
`therefore h_2 = h xx (-2) = -2.5 xx 2`
`therefore h_2 = -5 cm`
Thus, image will be real, inverted and enlarged .
`rArr` When candle is taken toward mirror, then image moves away and away from mirror. Hence, screenis also taken away with it. So, when `u rarr f`, then `v rarr oo`
`rArr ` When candle is taken to mirror at less than 18 cm, l.hen its image will be virtual and erect, so it cannot be obtained on screen.