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(a) Calculate the distance of an object of height h from a concave mirror of radius of curvature 20 cm, so as to obtain a real image of magnification 2. Find the location of image also.(b) Using mirror formula, explain why does a convex mirror always produce a virtual image. |
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Answer» Solution :(a) As per question the radius of curvature of concave mirror R = - 20 cm, hence its FOCAL LENGTH `f=R/2 = -10 cm` and magnification of real image `m=-2` As `m=-v/u`, hence, `-v/u =-2` or `v=2u` So, from mirror FORMULA `1/v+ 1/u = 1/f`, we have `1/(2u) + 1/u = 1/(-10) rArr 3/(2u) =-1/10 rArr u=-15 cm` and `v= 2u = 2 xx (-15) = -30 cm` Thus, the object is PLACED in front of mirror at a distance of 15 cm from it and its real, magnified and inverted image is formed at a distance of 30 cm in front of the mirror. (b) For a convex mirror `1/v = 1/f -1/u` but f is positive and u is negative i.e., `1/v = 1/f -1/(-u) = 1/f + 1/u = =ve` Therefore, irrespective of the value of u, value of v is ALWAYS +ve. It means that the image formed by convex mirror is always virtual independent of the location of the object. |
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