Diffraction pattern from a single slit of width 0.25 mm is observed with light of wavelength 5890 mathringA. Angular separation between first order minimum and third order maximum, falling on the same side, is

Question

Diffraction pattern from a single slit of width 0.25 mm is observed with light of wavelength 5890 mathringA. Angular separation between first order minimum and third order maximum, falling on the same side, is (A) 5.89 × 10-3 rad (B) 5.89 × 10-7 rad (C) 5.89 × 10-10 rad (D) 5.89 × 10-4 rad

Tardigrade Admin · Accepted Answer

In single slit diffraction pattern, positions of secondary maxima and minima are given by,

θ_{ma x} = \pm (2 n + 1) \frac{λ}{2 d}

and

θ_{min} = \pm n \frac{λ}{d}

, respectively.

∴ θ_{1 min} = \frac{λ}{d}

and

θ_{3 ma x} = \frac{7 λ}{2 d}

Angular separation

= θ_{3 ma x} - θ_{1 min} = \frac{7 λ}{2 d} - \frac{λ}{d}

= \frac{5 λ}{2 d} = \frac{5}{2} \times \frac{5890 \times 1 0 ^{- 10}}{0.25 \times 1 0 ^{- 3}} = 5.89 \times 1 0^{- 3}

rad.

Q. Diffraction pattern from a single slit of width $0.25 mm$ is observed with light of wavelength $5890 \overset{˚}{A}$ . Angular separation between first order minimum and third order maximum, falling on the same side, is

$5.89 \times 1 0^{- 3}$ rad

$5.89 \times 1 0^{- 7}$ rad

$5.89 \times 1 0^{- 10}$ rad

$5.89 \times 1 0^{- 4}$ rad

Q. Diffraction pattern from a single slit of width 0.25mm is observed with light of wavelength 5890A˚. Angular separation between first order minimum and third order maximum, falling on the same side, is

5.89×10−3 rad

5.89×10−7 rad

5.89×10−10 rad

5.89×10−4 rad

Q. Diffraction pattern from a single slit of width $0.25 mm$ is observed with light of wavelength $5890 \overset{˚}{A}$ . Angular separation between first order minimum and third order maximum, falling on the same side, is

$5.89 \times 1 0^{- 3}$ rad

$5.89 \times 1 0^{- 7}$ rad

$5.89 \times 1 0^{- 10}$ rad

$5.89 \times 1 0^{- 4}$ rad