2. Define refraction of light, Draw a ray diagram for refraction at a
spherical surface separating two media. For refraction at a spherical
surface derive the relation
12
ni
nz- ni
2
in object distance. (u) image distance (v)
refractive index of media (n1, n,) and radius of curvature (R)
u
R
Answers
Answer: 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: Radius
Using geometry,
i=x+y..............(i)
r=y−z..............(ii)
Using snell's law,
n
1
sini=n
2
sinr
n
1
sin(x+y)=n
2
sin(y−z)...............(iii) using (i) and (ii)
Using approximation, sin(x+y)≈x+y≈sinx+siny
sin(y−z)≈y−z≈siny−sinz
Using definition of sinusoid,
sinx≈
u
MN
sinz≈
v
MN
siny≈
R
MN
Using above approximations, equation (iii) can be rewritten as:
n
1
(
u
MN
+
R
MN
)=n
2
(
R
MN
−
v
MN
)
Rearranging the terms, we get:
u
n
1
+
v
n
2
=
R
n
2
−n
1
Applying sign convention, u→−u
v→+v
R→+R
v
n
2
−
u
n
1
=
R
n
2
−n
1
solution
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