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Question

# Define refraction of light waves.Draw a ray diagram for refraction at a spherical separating two media. For refraction at a spherical surface, derive the relation n2v−n1u=n2−n1R in object distance (u), image distance (v), refractive index of media (n1,n2) and radius of curvature (R).

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Solution

## When light ray enters a medium of different refractive index from another medium, it undergoes change of velocity. This is known as refraction of light. This change in velocity happens both in direction and magnitude of the light wave.Assumption:i and r are small⟹x,y,z are small⟹MN≈ length of arc (l) OM≈u: Object distance IM≈v: Image distance Cm≈R: RadiusUsing geometry, i=x+y..............(i)r=y−z..............(ii)Using snell's law,n1sini=n2sinr n1sin(x+y)=n2sin(y−z)...............(iii) using (i) and (ii)Using approximation, sin(x+y)≈x+y≈sinx+siny sin(y−z)≈y−z≈siny−sinzUsing definition of sinusoid, sinx≈MNusinz≈MNvsiny≈MNRUsing above approximations, equation (iii) can be rewritten as:n1(MNu+MNR)=n2(MNR−MNv)Rearranging the terms, we get:n1u+n2v=n2−n1RApplying sign convention, u→−u v→+v R→+Rn2v−n1u=n2−n1R

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