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# Lens Formula Assignment Help

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Optical Physics - Lens Formula

**Lens Formula**

It is a relation between focal length of a lens and distances of object and image from optical centre of the lens.

To derive this formula, we use the same new Cartesian sign conventions.

**(a) Convex lens:** the image formed may be virtual or real.

Real image: let C be the optical centre and F be the principle focus of a convex lens of focal length **CF = ƒ**.

AB is an object held perpendicular to the principle axis of the lens at a distance beyond focal length of the lens. A real, inverted and magnified image A’B’ is formed.

As ?s A’B’C and ABC are similar,

Therefore, **A’B’/AB = CB’/CB (1)**

Again as **?s A’B’F** and **CDF** are similar

Therefore, **A’B’/CD = B’F/CF (2)**

From (1) and (2),

**C****B’/CB = B’F/CF = (CB’ + CF)/CF**

Using new Cartesian sign conventions, let

**CB = -u, CB’ = -v, CF= +ƒ**

Therefore, **-v/-u = (-v + ƒ)/ƒ**

**uv – uƒ = - vƒ**

Divide both sides by **uvƒ**

**uv/ uvƒ = (uƒ/ uvƒ) – (vƒ/uvƒ)**

Or, **1/ƒ = (1/v – 1/u)**

This is the required lens formula.

Concave lens: in this case, the image formed is always virtual. Let C be the optical centre and F be the principle focus of a concave lens of focal length ƒ.

AB is an object held perpendicular to the principle axis of the lens. A virtual, erect and smaller image A’B’ is formed due to refraction through concave lens as shown in fig. 3

As ?s A’B’C and ABC are similar,

Therefore, **A’B’/AB = B’F/CF (3)**

Again as **?s A’B’F and CDF** are similar,

Therefore, **A’B’/CD = B’F/CF**

But **CD = AB**,

Therefore, **A’B’/AB = B’F/CF (4)**

From (3) and (4),

**CB’/CB = B’F/CF = (CF – CB’)/CF (5)**

Using new Cartesian sign conventions, let

CB = -u, CB’ = - v,

CF = - ƒ

-v/-u = (-ƒ + v)/-ƒ

Vƒ = uƒ – uv

Uv = uƒ – vƒ

Divide both sides by **uvƒ**

**uv/ uvƒ = (uƒ/uvƒ – vƒ/uvƒ)**

**1/ƒ = 1/v = 1/u**, this is the required formula.

ExpertsMind.com - Physics Help, Optical Physics Assignments, Lens Formula Assignment Help, Lens Formula Homework Help, Lens Formula Assignment Tutors, Lens Formula Solutions, Lens Formula Answers, Optical Physics Assignment Tutors

**Lens Formula**

To derive this formula, we use the same new Cartesian sign conventions.

**(a) Convex lens:**the image formed may be virtual or real.

Real image: let C be the optical centre and F be the principle focus of a convex lens of focal length

**CF = ƒ**.

AB is an object held perpendicular to the principle axis of the lens at a distance beyond focal length of the lens. A real, inverted and magnified image A’B’ is formed.

As ?s A’B’C and ABC are similar,

Therefore,

**A’B’/AB = CB’/CB (1)**

Again as

**?s A’B’F**and

**CDF**are similar

Therefore,

**A’B’/CD = B’F/CF (2)**

From (1) and (2),

**C**

**B’/CB = B’F/CF = (CB’ + CF)/CF**

Using new Cartesian sign conventions, let

**CB = -u, CB’ = -v, CF= +ƒ**

Therefore,

**-v/-u = (-v + ƒ)/ƒ**

**uv – uƒ = - vƒ**

Divide both sides by

**uvƒ**

**uv/ uvƒ = (uƒ/ uvƒ) – (vƒ/uvƒ)**

Or,

**1/ƒ = (1/v – 1/u)**

This is the required lens formula.

Concave lens: in this case, the image formed is always virtual. Let C be the optical centre and F be the principle focus of a concave lens of focal length ƒ.

AB is an object held perpendicular to the principle axis of the lens. A virtual, erect and smaller image A’B’ is formed due to refraction through concave lens as shown in fig. 3

As ?s A’B’C and ABC are similar,

Therefore,

**A’B’/AB = B’F/CF (3)**

Again as

**?s A’B’F and CDF**are similar,

Therefore,

**A’B’/CD = B’F/CF**

But

**CD = AB**,

Therefore,

**A’B’/AB = B’F/CF (4)**

From (3) and (4),

**CB’/CB = B’F/CF = (CF – CB’)/CF (5)**

Using new Cartesian sign conventions, let

CB = -u, CB’ = - v,

CF = - ƒ

-v/-u = (-ƒ + v)/-ƒ

Vƒ = uƒ – uv

Uv = uƒ – vƒ

CB = -u, CB’ = - v,

CF = - ƒ

-v/-u = (-ƒ + v)/-ƒ

Vƒ = uƒ – uv

Uv = uƒ – vƒ

Divide both sides by

**uvƒ**

**uv/ uvƒ = (uƒ/uvƒ – vƒ/uvƒ)**

**1/ƒ = 1/v = 1/u**, this is the required formula.

ExpertsMind.com - Physics Help, Optical Physics Assignments, Lens Formula Assignment Help, Lens Formula Homework Help, Lens Formula Assignment Tutors, Lens Formula Solutions, Lens Formula Answers, Optical Physics Assignment Tutors