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If a point source is placed at a distance of 18 cm from the pole of a concave mirror, its image is formed at a distance of 9 cm from the mirror. A glass slab of thickness 6 cm is placed between the point source and the mirror such that the parallel faces of the glass slab remains perpendicular to the principal axis of the mirror. If the refractive index of glass is 1.5 what will be the displacement of the image? |
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Answer» Solution :Let P be the position of the object and in the absence of the glass slab, Q be the position of image formed by the concave MIRROR [Fig. 2.23]. Here, `mu = 18` `OQ = v = 9 cm` `therefore " " "According to" (1)/(v) + (1)/(u) = (1)/(f) "we get"` `(1)/(-9) + (1)/(-18) = (1)/(f) or, f = - 6cm` If the slab of thickness 6 cm is PLACED between the point source and the concave mirror, apparent displacement of the point source will take place towards the mirror. The RAYS coming from P appear to come from P. after refraction. Apparent displacement of P. `PP. = d(1-(1)/(mu)) = 6(1-(1)/(1.5)) = 2cm` So in the second case, object distanceu = -(18 - 2) = - 16cm, f = - 6 cm , v = ? `"We know" , (1)/(v) + (1)/(u) = (1)/(f) or, (1)/(v) + (1)/(-16) = (1)/(-6)` `or, "" (1)/(v) = (1)/(-6) + (1)/(16) = (-10)/(96) or, v = -(96)/(10) = - 9.6cm` `therefore "" |OQ.| = 9.6` `therefore " " "Displacement of the image".` `Q Q. = OQ. - OQ = 9.6 - 9 = 0.6cm` |
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