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derivation of lens maker formula of thin lens

Asked by Shubham(student) , on 20/3/14


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Refraction by a Lens

Figure (a)

Figure (b)

Figure (c)

The above figure shows the image formation by a convex lens.

Assumptions made in the derivation:

  • The lens is thin so that distances measured from the poles of its surfaces can be taken as equal to the distances from the optical centre of the lens.

  • The aperture of the lens is small.

  • The object consists only of a point lying on the principle axis of the lens.

  • The incident ray and refracted ray make small angles with the principle axis of the lens.

A convex lens is made up of two convex spherical refracting surfaces.

The first refracting surface forms image I of the object O [figure (b)].

Image I1 acts as virtual object for the second surface that forms the image at I [figure (c)]. Applying the equation for spherical refracting surface to the first interface ABC, we obtain

A similar procedure applied to the second interface ADC gives

For a thin lens, BI1 = DI1

Adding equations (i) and (ii), we obtain

Suppose the object is at infinity i.e.,

OB → ∞ and DI → f

Equation (iii) gives

The point where image of an object placed at infinity is formed is called the focus (F) of the lens and the distance f gives its focal length. A lens has two foci, F and , on either side of it by the sign convention.

BC1 = R 1

CD2 = −R 2

Therefore, equation (iv) can be written as

Equation (v) is known as the lens maker’s formula.

From equations (iii) and (iv), we obtain

As B and D both are close to the optical centre of the lens,

BO = − u, DI = + v, we obtain

Equation (vii) is known as thin lens formula.

Posted by Sanjeev A.r(student)on 15/2/12

More Answers

 lence makers formula

Posted by Rizvan(student)on 7/11/12

 what is lence

Posted by Rizvan(student)on 7/11/12

It is the lens maker's formula where lens is the convex lens in this case. We have taken the convex lens to prove this formula and make sure that these are very thin lenses.

Lence is a non-existent word.

Posted by Aeross(student)on 16/11/13

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Figure (a)

Figure (b)

Figure (c)

The above figure shows the image formation by a convex lens.

Assumptions made in the derivation:

  • The lens is thin so that distances measured from the poles of its surfaces can be taken as equal to the distances from the optical centre of the lens.

  • Theaperture of the lens is small.

  • The object consists only of a point lying on the principle axis of the lens.

  • The incident ray and refracted ray make small angles with the principle axis of the lens.

A convex lens is made up of two convex spherical refracting surfaces.

The first refracting surface forms image I of the object O [figure (b)].

Image I1acts as virtual object for the second surface that forms the image at I [figure (c)]. Applying the equation for spherical refracting surface to the first interface ABC, we obtain

A similar procedure applied to the second interface ADC gives

For a thin lens, BI1= DI1

Adding equations (i) and (ii), we obtain

Suppose the object is at infinity i.e.,

OB→and DI→f

Equation (iii) gives

The point where image of an object placed at infinity is formed is called the focus(F) of the lens and the distancefgives its focal length. A lens has two foci,Fand, on either side of it by the sign convention.

BC1=R1

CD2= R2

Therefore,equation (iv) can be written as

Equation (v) is known as the lens makers formula.

From equations (iii) and (iv), we obtain

As B and D bothare close to the optical centre of the lens,

BO = u, DI = +v, we obtain

Equation (vii) is known as thin lens formula.

Posted by Adyant(student)3 weeks, 1 day ago

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