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A real image obtained by a concave mirror is 4 times bigger than the object. If the object is displaced by 3 cm away from the mirror, the image size becomes 3 times the object size. Find the focal length of the mirror. |
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Answer» SOLUTION :`rArr`Here, magnification of image m = - 4 New magnification of image m = -3 Focal lenght f = ? Focallenght f= ? AS per Gauss FORMULA `1/f = 1/v + 1/u` `thereforeu/f = (1)/(-m) + 1` `therefore u/f = 1 (1)/(m) "" (therefore m= -4)` `thereforeu/f = 1 - (1)/(-4)` `thereforeu/f=1 + (1)/(4)` `therefore u/f = 5/4`..........(1) `rArr` When object is placed 3 cm away from mirror, `therefore(u+3)/(f) = 1+ (1)/(3)` `therefore(u+3)/(f) = (4)/(3)` `thereforeu/f + 3/f = 4/3` `therefore5/4 + 3/f = 4/3` [ From (1)] `therefore3/f = 4/3 - 5/4` `therefore 3/f = (16-15)/(12)` `therefore3/f = 1/12therefore f = 36 cm = 360 cm ` |
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