Question

derive lens maker's formula assuming formula for refraction on curved surfaces​

Answer 1

➜Consider a convex lens (or concave lens) of absolute refractive index to be placed in a rarer medium of absolute refractive index. Considering the refraction of a point object on the surface XP

1

Y, the image is formed at I

1

;who is at a distance of V

1

.

CI

1

=PI

1

=V

1

(asthelensisthin)

CC

1

=PC

1

=R

1

CO=P

1

O=u

It follows from the diffraction due to convex spherical surfaceXP

1

Y

(

−u

μ

1

)+(

v

1

μ

2

)=(

R

1

μ

2

−μ

1

)...(1)

the refracted ray from A suffers a second refraction on the surface XP

2

Y and emerges along BI . Therefore I is the final real image of O .

Here the object distance is

u=CI

1

≃P

2

I

1

=V

Note that lens thickness is very small. It follows from the refraction due to convex spherical surface XP

1

Y

CI≃P

2

I=V

(−

v

1

μ

2

)+(

v

μ

2

)=(−

R

2

μ

2

−μ

1

)...(2)

v

1

−

u

1

=

f

1

...(3)

adding equation (1) and (2)

⇒μ

1

[

v

1

−

u

1

]=μ

2

−μ

1

[

R

1

1

−

R

2

1

]

⇒

v

1

−

u

1

=

μ

1

μ

2

−μ

1

[

R

1

1

−

R

2

1

]

⇒

f

1

=

μ

1

μ

2

−μ

1

[

R

1

1

−

R

2

1

]

(replaced by equation (3))

using

μ

1

μ

2

=μ

⇒

f

1

=(μ−1)[

R

1

1

−

R

2

1

] this is called lens maker formula.

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#THE GREAT SHREYA ❤️