**Topic — Lens Maker’s Formula **

## Formula Used

### 1. When a lens of refractive index μ_{2} is placed in a medium of refractive index μ_{1 }then

### 1/f = (μ_{21}-1)[1/R_{1}-1/R_{2}]

### OR

1/f = [(μ_{2}/μ1)-1][1/R_{1}-1/R_{2}]

## 2. When the lens is placed in the air then μ_{1} = 1 and μ_{2} = μ then

### 1/f = (μ-1)[1/R_{1}-1/R_{2}]

#### Sign Convention

#### 1 ) For Convex lens —

f = +ve

R1 = +ve

R2 = -ve

#### 2 ) For Concave lens —

f = -ve

R1 = -ve

R2 = +ve

Questions for practice —

**Level 1**

Q.1 The radii of curvature of a double convex lens are 15cm and 30cm and its refractive index is 1.5. Calculate its focal length. [20cm]

Q.2 The radius of curvature of each face of the biconcave lens, made of glass of refractive index 1.5 is 30 cm. Calculate the focal length of the lens in air. [-30 cm]

Q.3 The radii of curvature of the faces of a double convex lens are 10cm and 15cm. If the focal length is 12cm, what is the refractive index of the glass? [1.5]

Q.4 A biconvex lens has a focal length 2/3 times the radius of curvature of either surface. Calculate the refractive index of the lens material. [1.75]

**Level 2**

**Note: The focal length of a Glass Slab / Plane glass is ∞ and its Power is zero.**

**The refractive index of glass, µ _{g}=3/2 or 1.5**

**The refractive index of water, µ _{w}=4/ or 1.33**

Q.1 A plano-convex lens µ =1.5 has a focal length of 18cm in air. Calculate the radius of curvature of the spherical surface. [9cm]

Q.2 An equiconvex lens of focal length 15cm is cut into two equal halves as shown in the figure. What is the focal length of each half? [30cm] **LEVEL 3**

Formula Used

f_{m}={[µ_{2}-1]/[(µ_{2}/µ_{1})-1]}×f_{a}

Where

f_{m}=focal length of the lens in medium

f_{a}=focal length of the lens in air

µ_{2} = Refractive index of the lens

µ_{1} = Refractive index of the medium outside the lens

Q.3 The focal length of a glass convex lens in the air is 15 cm. Calculate its focal length, when it is totally immersed in water. [ 60 cm]

Q.4 A convex lens of focal length 2cm and refractive index 1.5 is immersed in a liquid of refractive index a) 1.6 b) 1.3 and c)1.5. What changes happen to the focal length of the lens in the three cases? [a) -16 b) + 6.5 c) ∞]

Q.5 A thin converging glass lens made of glass with a refractive index of 1.5 has a power of + 5.0 D. When this lens is immersed in a liquid of refractive index n, it acts as a diverging lens of focal length 100 cm. What must be the value of n? [1.6]

Q.6 The radius of curvature of each surface of a convex lens is 20 cm and the refractive index of the material of the lens is 3/2.

a) Calculate its focal length.

b) If this is cut along the plane AB, what will be the focal length of each of the two halves formed?

c) What happens if the lens is cut along the CD.

[20cm, 40cm, f remains the same but intensity decreases.]