Question

Draw ray diagrams to show the process of refraction of light at different Curved Surfaces.
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Answer 1

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

Answered By=shreyash. .........