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$$2=1.5$$   $$r=+30cm$$,$$u=$$−$$40cm$$                ∵μ$$2v$$−μ$$1u=$$μ$$2$$−μ$$1t$$                         Or $$1.5v$$−$$1.2$$−$$40=1.5$$−$$1.230$$  or  $$1.5v+12400=3300$$            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,t'$$=-30$$                ∴μ$$2$$'v'−μ$$1$$'u'$$=$$μ$$2$$'−μ$$1$$'t            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.

Detailed Solution

Get Expert Academic Guidance – Connect with a Counselor Today!