In a single slit diffraction pattern, a light of wavelength 6000 is used. The distance between the first and third minima in the diffraction pattern is found to be 3 mm when the screen is placed 50 cm away from the slits. The width of the slit is ____m.

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
In a single slit diffraction pattern, a light of wavelength 6000 $Å$ is used. The distance between the first and third minima in the diffraction pattern is found to be 3 mm when the screen is placed 50 cm away from the slits. The width of the slit is ____ $\times 10^{- 4}$ m. [2024]

Ans.
(2)

For $n^{t h}$ minima $b \sin θ = n λ$

( $λ$ is small so sin $θ$ is small, hence b tan $θ$ = $n λ$ )

$b \tan θ = n λ$

$b \frac{y}{D} = n λ$

$\Rightarrow y_{n} = \frac{n λ D}{b}$ (Position of $n^{t h}$ minima)

$B \to 1^{s t}$ minima, $A \to 3^{r d}$ minima

$y_{3} = \frac{3 λ D}{b}, y_{1} = \frac{λ D}{b}$

$Δ y = y_{3} - y_{1} = \frac{2 λ D}{b}$

$3 \times 10^{- 3} = \frac{2 \times 6000 \times 10^{- 10} \times 0.5}{b}$

$b = \frac{2 \times 6000 \times 10^{- 10} \times 0.5}{3 \times 10^{- 3}} = 2 \times 10^{- 4} m$

$x = 2$

Want Us to Email you About Special Offers & Updates?