Question

Focal length of the plano-convex lens is ...... when its radius of curvature of the surface is R and n is the refractive index of the lens

Answer 1

Figure shows a plano-convex lens of refractive index

μ

=

n

.

From Lens Maker's formula:-

1

f

=

(

μ

2

μ

1

−

1

)

(

1

R

1

−

1

R

2

)

where,

μ

2

and

μ

1

are refractive index of lens and surrounding medium respectively.

And,

R

1

and

R

2

are radius of 1st and 2nd surfaces respectively.

Here,

μ

1

=

1

,

μ

2

=

n

,

R

1

=

−

∞

,

R

2

=

−

R

,

f

=

2

R

Hence,

1

f

=

(

n

−

1

)

(

1

−

∞

−

1

−

R

)

⟹

1

f

=

(

n

−

1

)

1

R

⟹

f

=

R

n

−

1