At the mouth of a cylindrical vessel, a convex lens of refractive index 1.5 and radius of curvature of curved surface 30 cm is filled. A point source S is at the bottom of vessel. The height of vessel is 40 cm and filled with liquid of refractive index 1.2. Find the position of image.

Question

Infinity Learn · Accepted Answer

For refraction through spherical surface, μ$$1=1.2$$, μ$$2=1.5$$   $$r=+30$$ cm, $$u=$$−$$40$$ cm                ∵μ$$2v$$−μ$$1u=$$μ$$2$$−μ$$1r$$                  Or,  $$1.5v$$−$$1.2$$−$$40=1.5$$−$$1.230$$⇒$$1.5v+12400=3300$$     Or, $$1.5v=1100$$−$$3100=-2100$$     Or,  $$v=$$−$$1002$$×$$1.5=$$−$$75$$ cm   For refraction through spherical surface, μ$$1$$'$$=1.5$$, μ$$2$$'$$=1$$, u'$$=-75$$ cm, r'$$=-30$$∴μ$$2$$'v'−μ$$1$$'u'$$=$$μ$$2$$'−μ$$1$$'r'Or, $$1v$$'$$+1.575=1-1.5-30$$   ∴v'$$=$$−$$300$$ cm

At the mouth of a cylindrical vessel, a convex lens of refractive index 1.5 and radius of curvature of curved surface 30 cm is filled. A point source S is at the bottom of vessel. The height of vessel is 40 cm and filled with liquid of refractive index 1.2. Find the position of image.

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