In the diffraction pattern, the first maximum | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The condition for the $n^{th}$ secondary maximum in a single-slit diffraction pattern is given by $a \sin 	heta = (n + \frac{1}{2}) \lambda$, whe

Vedclass · Accepted Answer

$3 \left( \frac{\sqrt{2} - 1}{\sqrt{2}} \right) \lambda$

Vedclass · Answer

(A) The condition for the $n^{th}$ secondary maximum in a single-slit diffraction pattern is given by $a \sin 	heta = (n + \frac{1}{2}) \lambda$, where $n = 1, 2, 3, \dots$For the first maximum, $n = 1$, so $a \sin 	heta = \frac{3}{2} \lambda$.Case $1$: $a_1 \sin 30^{\circ} = \frac{3}{2} \lambda \implies a_1 (\frac{1}{2}) = \frac{3}{2} \lambda \implies a_1 = 3 \lambda$.Case $2$: $a_2 \sin 45^{\circ} = \frac{3}{2} \lambda \implies a_2 (\frac{1}{\sqrt{2}}) = \frac{3}{2} \lambda \implies a_2 = \frac{3\sqrt{2}}{2} \lambda = \frac{3}{\sqrt{2}} \lambda$.The change in slit width is $\Delta a = a_1 - a_2 = 3 \lambda - \frac{3}{\sqrt{2}} \lambda = 3 \lambda (1 - \frac{1}{\sqrt{2}}) = 3 \lambda \left( \frac{\sqrt{2} - 1}{\sqrt{2}} ight)$.

In the diffraction pattern, the first maximum is at $30^{\circ}$, when a monochromatic light of wavelength $\lambda$ is incident on a slit of width $a$. For the same wavelength, if the slit width is changed, so that the first maximum is at $45^{\circ}$, by how much is the slit width changed?

Similar Questions

$A$ beam of light of $\lambda = 600 \, nm$ from a distant source falls on a single slit $1 \, mm$ wide and the resulting diffraction pattern is observed on a screen $2 \, m$ away. The distance between the first dark fringes on either side of the central bright fringe is:

Which scientist discovered the phenomenon of diffraction of light?

Obtain the formulas for the angular width and linear width of the central maximum in a single-slit diffraction experiment.

In a diffraction pattern produced by a thin wire,what happens to the fringe width when the diameter of the wire is increased?

$A$ slit of width $a$ is illuminated by white light. For red light $(\lambda = 6500 \; \mathring{A})$,the first minima is obtained at $\theta = 30^\circ$. Then the value of $a$ will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module