In a diffraction pattern due to a single slit of width , the first minimum is observed at an angle when light of wavelength 5000 is incident on the slit. The first secondary maximum is observed at an angle of [2016]

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

Q.
In a diffraction pattern due to a single slit of width $a$ , the first minimum is observed at an angle $30 °$ when light of wavelength 5000 $Å$ is incident on the slit. The first secondary maximum is observed at an angle of [2016]

1 $\sin^{- 1} (\frac{1}{2})$

2 $\sin^{- 1} (\frac{3}{4})$

3 $\sin^{- 1} (\frac{1}{4})$

4 $\sin^{- 1} (\frac{2}{3})$

Ans.
(2)

For first minimum, the path difference between extreme waves, $a \sin θ = λ$

Here $θ = 30 ° \Rightarrow \sin θ = \frac{1}{2} ∴ a = 2 λ$ ...(i)

For first secondary maximum, the path difference between extreme waves

$a \sin θ' = \frac{3}{2} λ or (2 λ) \sin θ' = \frac{3}{2} λ [Using eqn (i)]$

or $\sin θ' = \frac{3}{4} ∴$ $θ' = \sin^{- 1} (\frac{3}{4})$

Solution

Q.
In a diffraction pattern due to a single slit of width $a$ , the first minimum is observed at an angle $30 °$ when light of wavelength 5000 $Å$ is incident on the slit. The first secondary maximum is observed at an angle of [2016]

1 $\sin^{- 1} (\frac{1}{2})$

2 $\sin^{- 1} (\frac{3}{4})$

3 $\sin^{- 1} (\frac{1}{4})$

4 $\sin^{- 1} (\frac{2}{3})$

Want Us to Email you About Special Offers & Updates?

Solution

Q. In a diffraction pattern due to a single slit of width a, the first minimum is observed at an angle 30° when light of wavelength 5000 Å is incident on the slit. The first secondary maximum is observed at an angle of [2016]

1 sin-1(12)

2 sin-1(34)

3 sin-1(14)

4 sin-1(23)

Ans. (2) For first minimum, the path difference between extreme waves, asinθ=λ Here θ=30°⇒sinθ=12 ∴a=2λ ...(i) For first secondary maximum, the path difference between extreme waves asinθ'=32λ or (2λ)sinθ'=32λ [Using eqn (i)] or sinθ'=34 ∴ θ'=sin-1(34)

Want Us to Email you About Special Offers & Updates?

Q.
In a diffraction pattern due to a single slit of width $a$ , the first minimum is observed at an angle $30 °$ when light of wavelength 5000 $Å$ is incident on the slit. The first secondary maximum is observed at an angle of [2016]

1 $\sin^{- 1} (\frac{1}{2})$

2 $\sin^{- 1} (\frac{3}{4})$

3 $\sin^{- 1} (\frac{1}{4})$

4 $\sin^{- 1} (\frac{2}{3})$