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InterviewSolution
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In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is : |
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Answer» 27.5 cm Object distance, `u= -20 cm ` Let the distance of the IMAGE formed by the lens from its optical centre be `V`. Using lens formula `1/f= 1/v -1/u` `1/v = 1/f +1/u= 1/15 - 1/20` `1/v = (4-3)/(60)` ` v = 60 cm ` The convex lens forms an image at a distance 60 cm, rightwards, the image is real and inverted  The final image can be formed on the object itself when the rays afterrefraction from the lens retracetheir paths. That is only possible here when the rays fall normally on the convex mirror. The rays directed TOWARDS the centre of curvature of the convex mirror are actually perpendicular to it and they retrace their paths. Hence, the image formed by the convex lens should lie at the the centre of curvature of the convex mirror. Image distance for lens = distance between the lens and the mirror `+` radius of curvature `60 cm = 5 cm + R` ` R = 55 cm` We KNOW the relation between focal length f and radius of curvature R `2f= 55 cm` ` f = 55//2 = 27.5cm` |
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