Question

The minimum deviations suffered by, yellow and violet beams passing through an equilateral transparent prism are 38.4°, 38.7° and 39.2° respectively. Calculate the dispersive power of the medium.

Answer 1

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0.018 will be the answer .

Answer 2

The dispersive power of the medium is $\omega=0.018$

Explanation:

Step 1:

For equilateral triangle angle of prism $A=60^{\circ}$

Refractive index can be calculated as

$\mu=\frac{\sin \frac{A+\delta}{2}}{\sin \frac{A}{2}}$

Where ,

A= angle of prism

δ = angle of minimum deviation

For red light $\delta=38.4^{\circ}$

Step 2:

$\mu_{r}=\frac{\sin \frac{60+38.4}{2}}{\sin \frac{60}{2}}$  (by substituting the value in above equation)

$\mu_{r}=1.514$  (refractive index for red light)

Step 3:

Similarly ,for yellow and violet light  we get the refractive index for  

Yellow light  $\mu_{y}=1.518$      

Violet light  $\mu_{v}=1.523$

Dispersive power $\omega=\frac{\mu_{v}-\mu_{r}}{\mu_{y}-1}$

$\mu_{v}$=refractive index for violet light

$\mu_{r}$=refractive index for red light

$\mu_{y}$=refractive index for yellow light

$\omega=\frac{1.523-1.514}{1.518-1}$

$\omega=0.018$

So the dispersive power of medium is $0.018$