Question

Consider Young’s double-slit experiment where the separation between the two slits is 0.125 mm. The slits are illuminated by a light of wavelength 4500 ${A^o}$ and the screen is placed at a distance 1 m away from the plane of the slits. Find the separation between the second bright fringes on either side of the central maxima.

Answer 1

Hint: The Young’s double-slit experiment with a separation $d$ between the slits produces equally spaced fringes. Thus the distance between the central maxima and the second bright fringe to its left is equal to the distance between the central maxima and the second bright fringe to its right.

Formula used:
The position of the nth bright fringe is given by, $x = \dfrac{{n\lambda D}}{d}$ where, $n = 0, \pm 1, \pm 2,....$ denotes the number of the fringe, λ is the wavelength of the light used, D is the distance between the screen and the plane of slits and d is the separation between the slits.

Complete step by step solution:
Step 1: List the data given in the question.
Given, the separation between the two slits is $d = 0.125{\text{mm}} = 0.125 \times {10^{ - 3}}{\text{m}}$ .
The slits are illuminated by a light of wavelength $\lambda = {{4500A^o}} = 4.5 \times {10^{ - 7}}{\text{m}}$ .
The screen is placed at a distance $D = 1{\text{m}}$ away from the plane of the slits.
 Step 2: Obtain the position of the second bright fringe on one side of the central maxima.
The expression for the position of the nth bright fringe is given by, $x = \dfrac{{n\lambda D}}{d}$ ------ (1).
For the second bright fringe on the left of the central maxima, $n = - 2$ .
Substituting the given quantities in equation (1) gives us $x = \dfrac{{n\lambda D}}{d} = \dfrac{{ - 2 \times \left( {4.5 \times {{10}^{ - 7}}} \right) \times 1}}{{0.125 \times {{10}^{ - 3}}}}$ .
Hence, the position of the second bright fringe on the left of the central maxima is ${x_{l2}} = - 7.2 \times {10^{ - 9}}{\text{m}}$ or ${x_{l2}} = - 7.2{\text{nm}}$ .
The negative sign merely indicates that it lies on the left of the central maxima.
Then the position of the second bright fringe on the right of the central maxima is ${x_{r2}} = 7.2 \times {10^{ - 9}}{\text{m}}$ or ${x_{r2}} = 7.2{\text{nm}}$ .
 Step 3: Calculate the separation between the second bright fringes on either side of the central maxima.
We have, ${x_{l2}} = - 7.2{\text{nm}}$ and ${x_{r2}} = 7.2{\text{nm}}$.
Then the separation between the two fringes will be ${x_{r2}} - {x_{l2}} = 7.2 - \left( { - 7.2} \right)=14.4nm$ .

$\therefore $ The separation between the second bright fringes on either side of the central maxima is 14.4 nm.

Additional Information:
In a Zener diode current flows in reverse as well as forward direction when the voltage exceeds break down voltage. This breakdown voltage is known as Zener voltage. Zener diode is widely used as a voltage regulator. Zener diode is also used to limit the current through the diode and drop the excess voltage in the conducting diode.

Note:
Zener diode is the special diode which works in reverse biased and breakdown regions. Zener diode is used as a voltage regulator. When a Zener diode is connected in forward bias then its characteristics are just the same as an ordinary diode.