Question

Write down the lens maker formula with complete explanation and diagram.​​

Answer 1

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Write down the lens maker formula with complete explanation and diagram.

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☆A lens is said to be thin if the gap between the two surfaces is very small. A lens will be converging with positive focal length, and diverging if the focal length is negative.

A lens is said to be thin if the gap between the two surfaces is very small. A lens will be converging with positive focal length, and diverging if the focal length is negative....

A lens is said to be thin if the gap between the two surfaces is very small. A lens will be converging with positive focal length, and diverging if the focal length is negative....Formula.

A lens is said to be thin if the gap between the two surfaces is very small. A lens will be converging with positive focal length, and diverging if the focal length is negative....Formula.f The focal length of the lens

A lens is said to be thin if the gap between the two surfaces is very small. A lens will be converging with positive focal length, and diverging if the focal length is negative....Formula.f The focal length of the lensμ Refractive index

A lens is said to be thin if the gap between the two surfaces is very small. A lens will be converging with positive focal length, and diverging if the focal length is negative....Formula.f The focal length of the lensμ Refractive indexR 1 a n d R 2 R_1 and R_2 R1andR2 the radius of the curvature of both surfaces

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•A lens formula may be defined as the formula which gives the relationship between the distance of image (v), distance of object (u), and the focal length (f) of the lens. It may be written as: Principal Axis Concave Lens. Where, v = Distance of image from optical centre of lens.

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Answer 2

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Write down the lens maker formula with complete explanation and diagram.

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From the above figure,

In ∆ABC,

$\frac{n1}{BO}$+$\frac{n2}{BI1}$= $\frac{n2-n1}{BC1}$

In ∆ADC,

$\frac{n2}{-DI1}$+$\frac{n1}{D1}$= $\frac{n1-n2}{-DC2}$

$\Large{\underline{\rm{\green{As \:the\: lens \:is\: very\: thin,}}}}$

$\Large{\underline{\rm{\green{B\:and\:D\: point\: can\: be\: taken \:as\: same.}}}}$

Therefore,

$\frac{n1}{BO}$+$\frac{n2}{BI1}$= $\frac{n2-n1}{BC1}$───────── ( i )

$\frac{n1}{BI}$-$\frac{n2}{BI1}$= $\frac{n2-n1}{BC2}$───────── ( ii )

Adding ( i ) and ( ii ),

$\frac{n1}{BI}$+$\frac{n1}{BO}$= n2-n1❴$\frac{1}{BC1}$+$\frac{1}{BC2}$❵

⇒$\frac{1}{BI}$+$\frac{1}{BO}$=$\frac{n2-n1}{nI}$ ❴$\frac{1}{BC1}$+$\frac{1}{BC2}$❵

Using sign convention,

• BI = v
• BC1 = R1
• BO = -u
• BC2 = -R2

⇒$\frac{1}{v}$+$\frac{1}{u}$=$\frac{n2-n1}{nI}$ ❴$\frac{1}{R1}$-$\frac{1}{R2}$❵

Now,

If u = ∝ and v = f,

⇒$\frac{1}{v}$-$\frac{1}{u}$=$\frac{1}{f}$

∴ $\frac{1}{f}$ = (n21 - 1)❴$\frac{1}{R1}$-$\frac{1}{R2}$❵

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