Download App

STD 12 - 10. Wave optics — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 10. Wave optics4 Marks
MCQ
Two coherent sources $S_1$ and $S_2$ are separated by a distance four times the wavelength $\lambda$ of the source. The sources lie along y axis whereas a detector moves along $+ x$ axis. Leaving the origin and far off points the number of points where maxima are observed is
  • A
    $2$
  • ✓
    $3$
  • C
    $4$
  • D
    $5$
✓

Answer

Correct option: B.
$3$
b
(b) From $\Delta {S_1}{S_2}D,$
${({S_1}D)^2} = {({S_1}{S_2})^2} + {({S_2}D)^2}$
${({S_1}P + PD)^2} = {({S_1}{S_2})^2} + {({S_2}D)^2}$
Here ${S_1}P$ is the path difference $ = n\lambda $ for maximum intensity.
$\therefore {(n\lambda + {x_n})^2} = {(4\lambda )^2} + {({x_n})^2}$
or ${x_n} = \frac{{16{\lambda ^2} - {n^2}{\lambda ^2}}}{{2n\lambda }}$
Then ${x_1} = \frac{{16{\lambda ^2} - {\lambda ^2}}}{{2\lambda }} = 7.5\,\lambda $
${x_2} = \frac{{16{\lambda ^2} - 4{\lambda ^2}}}{{4\lambda }} = 3\lambda $
${x_3} = \frac{{16{\lambda ^2} - 9{\lambda ^2}}}{{6\lambda }} = \frac{7}{6}\lambda $
${x_4} = 0$.
$\therefore $Number of points for maxima becomes $ 3$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A bar magnet of length $10 \,cm$  and having the pole strength equal to $10^{-3}$ weber is kept in a magnetic field having magnetic induction $ (B)$  equal to $4\pi \times {10^{ - 3}}$ Tesla. It makes an angle of $30°$  with the direction of magnetic induction. The value of the torque acting on the magnet is
→
One mole of diatomic ideal gas undergoes a cyclic process $ABC$ as shown in figure. The process $BC$ is adiabatic. The temperatures at $A, B$ and $C$ are $400\,K, 800\,K$ and $600\,K$ respectively. Choose the correct statement
→
$5$ amperes of current is passed through a metallic conductor. The charge flowing in one minute in coulombs will be
→
A charge $Q\;\mu C$ is placed at the centre of a cube, the flux coming out from any surfaces will be
→
When a load of $10 \,kg$ is suspended on a metallic wire, its length increase by $2 \,mm$. The force constant of the wire is $........ N / m$
→
The momentum $p$ of an object varies with time $(t)$ as shown in figure. The corresponding force $(F)$-time $(t)$ graph is
→
The mechanism of the hydrogen bomb is based on
→
Two capillary tubes $  P$ and $Q$ are dipped in water. The height of water level in capillary $P$ is $2/3$ to the height in $Q$ capillary. The ratio of their diameters is
→
By placing the prism in minimum deviation position, images of the spectrum
→
A resistance is shown in the figure. Its value and tolerance are given respectively by
→