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A WATER TANK HAS A SMALL SPHERICAL WINDOW OF RADIUS OF CURVATURE 15CM..THE CONVEX SURFACE OF WINDOW IS OUTSIDE OF TANK . A POINT OBJECT IS PLACED AT A DISTANCE OF 60CMS FROM THE WINDOW IN AIR.FIND THE IMAGE DISTANCE
Asked by neetaspirantdoctor | 14 May, 2022, 10:59: PM
First figure shows the refraction taking place when light rays from object O incident on front surface of glass window.
Light rays enters from air ( n1 = 1 )  to glass ( n2 = 1.5 ), where n represents refractive index

Image distance is determined from the following equation for refraction at spherical surace .

................................(1)
where v = image distance = AI1
u = object distance = AO = -60 cm
R = radius of curvature = 15 cm

From above expression , we get AI1 = 90 cm

Now first image I1 is acting as object for the spherical surface of window which is inside water.

Light rays enters from water ( n2 = 1.333 )  to glass ( n1 = 1.5 ), where n represents refractive index

Image distance is determined from eqn.(1) by using proper sign convention

We get final image distance BI2 = 45 cm from above expression
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