Question

Find the intensity on the screen at O if $S_1$ and $S_3$ are covered.

• A. $\frac{I_0}{\sqrt{7}}$
• B. $\frac{I_0}{7}$
• C. $\frac{I_0}{\sqrt{6}}$
• D. $\frac{I_0}{6}$

Answer 1

Answer: (B)

$\frac{I_0}{7}$

Answer 2

Let the amplitude of the wave from each slit at point O be $a$. Since O is the central point and the incident wavefronts are plane, the waves from the three identical slits $S_1, S_2, S_3$ arrive at O in phase.

When all three slits are open, the resultant amplitude at O is the sum of the individual amplitudes: $A_{total} = a + a + a = 3a$.

The intensity is proportional to the square of the amplitude. The intensity when all three slits are open is given as $I_0$.

So, $I_0 \propto (3a)^2 = 9a^2$. Let $I_0 = k (9a^2)$ for some constant $k$. The intensity from a single slit at O would be $I_1 = k a^2$.

From $I_0 = 9ka^2$, we get $ka^2 = I_0/9$. Thus, the intensity from a single slit is $I_1 = I_0/9$.

If $S_1$ and $S_3$ are covered, only slit $S_2$ is open. The amplitude at O is the amplitude from $S_2$, which is $a$.

The intensity at O is $I_{S_2} = k a^2 = I_0/9 \approx 0.111 I_0$.

Among the given options, $\frac{I_0}{7} \approx 0.143 I_0$ is the closest value to $I_0/9$.