In a Young's double slit experiment, the separation between the two slits is and the wavelength of the light is . The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the correct choice(s).

Question

In a Young's double slit experiment, the separation between the two slits is $d$ and the wavelength of the light is $λ$ . The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the correct choice(s). [2008]

Smart Achievers · Accepted Answer

(1, 2)

Condition to obtain maxima in Young's double slit experiment is

$d \sin θ = n λ$ where $n$ is an integer.

(1) When $d = λ$

$λ \sin θ = n λ$ $\Rightarrow \sin θ = n$

When $n = 0, θ = 0$

When $n = 1, θ = 90 °$

(This will be a point on the screen which will be at infinity and therefore not practical.)

Other values of $n$ are invalid as $- 1 \leq \sin θ \leq 1 .$

Hence, only one maxima when $d = λ .$

(2) When $λ < d < 2 λ$

$\Rightarrow λ < \frac{n λ}{\sin θ} < 2 λ$ $(∵ d = \frac{n λ}{\sin θ})$

$\Rightarrow 1 < \frac{n}{\sin θ} < 2$

$∴$ $Possible values of n are 0, + 1, - 1$

Hence, there is at least one more maxima besides the central maxima.

As we know,

$I_{\max} = {(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2}$ and $I_{\min} = {(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2}$

Initially, $I_{1} = 4 I$ and $I_{2} = I$

$∴$ $I_{\max} = 9 I$ and $I_{\min} = I$

When $I_{1} = I_{2} = I$ then $I_{\max} = 4 I$ and $I_{\min} = 0$

i.e., when the intensities become equal, $I_{\min}$ reduces to zero.

Solution

Q.
In a Young's double slit experiment, the separation between the two slits is $d$ and the wavelength of the light is $λ$ . The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the correct choice(s). [2008]

1 If $d = λ$ , the screen will contain only one maximum

2 If $λ < d < 2 λ$ , at least one more maximum (besides the central maximum) will be observed on the screen

3 If the intensity of light falling on slit 1 is reduced so that it becomes equal to that of slit 2, the intensities of the observed dark and bright fringes will increase

4 If the intensity of light falling on slit 2 is increased so that it becomes equal to that of slit 1, the intensities of the observed dark and bright fringes will increase

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