Question

A point is situated at 7cm and 7.2cm from two coherent sources. Find the nature of illumination at the point if the wavelength of light is 4000Å.

Answer 1

Hint: Nature of illumination (constructive or destructive) at a point depends on the path difference between the sources.

Formula Used:
Path difference for constructive interference:
$p=n\lambda$ …… (1)
Path difference for destructive interference
$p={\displaystyle \frac{(2n+1)}{2}}\lambda$ …… (2)
where,
p is the path difference between the 2 sources
n is an integer
$\lambda$ is the wavelength of light.

Complete step by step answer:

Given:
1. Distance of source1 from point (s1) =7cm.
2. Distance of source2 from point (s2) =7.2cm
3. Wavelength of light ($\lambda$) = 4000Å.

To find: Nature of illumination at the point.

Step 1 of 3:
When the path difference between two coherent sources is an integral multiple of wavelength of light, we see constructive interference at that point. A bright spot is obtained in this case.
When the path difference between two coherent sources is an odd multiple of half the wavelength of light, we see destructive interference at that point. A dark spot is obtained in this case.

Step 2 of 3:
Calculate the path difference:
$p=s_2-s_1$
$p=(7.2-7)cm$
$p=0.2cm$

Step 3 of 3:
Put the values of p and $\lambda$ in equation (1):
$$\begin{gathered} 0.2=n\times 4000\times {10}^{-10} \\ n={\displaystyle \frac{0.2}{4000\times {10}^{-10}}} \\ n=500000 \end{gathered}$$

As n obtained is an integer, we can conclude that there is constructive interference at the point and a bright spot is obtained.

Final Answer: The nature of illumination at the point is a bright spot due to constructive interference.

Note: In questions where we have to find the nature of illumination, divide the path difference by the wavelength and check if the number (n) obtained is an integer or not.