A parallel beam of white light falls on a convex lens, images of blue, yellow and red light are formed on other side of the lens at distances 20 cm, 20.5 cm and 21.4 cm respectively. The disperssive power of the material of the lens is :

Question

A parallel beam of white light falls on a convex lens, images of blue, yellow and red light are formed on other side of the lens at distances 20 cm, 20.5 cm and 21.4 cm respectively. The disperssive power of the material of the lens is : (A)  (5/214)  (B)  (14/205)  (C)  (619/1000)  (D)  (5/205)

Tardigrade Admin · Accepted Answer

The refractive index of the material of the lens and hence, the focal length of the lens is different for different colours known as chromatic aberration.
The expression for chromatic aberration is

f_{R} - f_{B} = ω f_{y}

where,

f_{R}, f_{B}

and

f_{Y}

are focal lengths of red, blue and yellow light and

ω

is dispersive power.
Putting the numerical values, we have

ω = \frac{f _{R} - f _{B}}{f _{Y}} = \frac{21.4 - 20}{20.5}

ω = \frac{14}{205}

Q. A parallel beam of white light falls on a convex lens, images of blue, yellow and red light are formed on other side of the lens at distances $20 c m, 20.5 c m$ and $21.4 c m$ respectively. The disperssive power of the material of the lens is :

$\frac{5}{214}$

$\frac{14}{205}$

$\frac{619}{1000}$

$\frac{5}{205}$

Q. A parallel beam of white light falls on a convex lens, images of blue, yellow and red light are formed on other side of the lens at distances 20cm,20.5cm and 21.4cm respectively. The disperssive power of the material of the lens is :

2145​

20514​

1000619​

2055​

Q. A parallel beam of white light falls on a convex lens, images of blue, yellow and red light are formed on other side of the lens at distances $20 c m, 20.5 c m$ and $21.4 c m$ respectively. The disperssive power of the material of the lens is :

$\frac{5}{214}$

$\frac{14}{205}$

$\frac{619}{1000}$

$\frac{5}{205}$