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Physics Ncert Solutions Class 12th Physics Class 12th Wave Optics

10.21 In deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of n $λ$ /a.

Justify this by suitably dividing the slit to bring out the cancellation.

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Payal Gupta | Contributor-Level 10

5 months ago

10.21 Consider that a single slit of width $d$ is divided in to $n$ smaller slits.

Therefore width of each slit,

$d^{'} = \frac{d}{n}$

Angle of diffraction is given by the relation,

$? = \frac{\frac{d}{d}}{d} ?$ = $\frac{?}{d}$

Now, each of these infinitesimally small slit sends zero intensity in the direction of Ø.

Hence, the combination of these slits will give zero intensity.

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A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wave-train of wavelength 6 cm is produced at the lower end of the rope. What is the wavelength of the wave train (in cm) when it reaches the top of the rope?

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At lower end
Tension, T? = 2g = 20 N (due to the 2 kg block)
Velocity, v? = √ (T? /μ) = √ (20/μ)
Wavelength, λ? = 6 cm

At upper end
Tension, T? = (2 kg + 6 kg)g = 8g = 80 N (due to the block and the rope)
Velocity, v? = √ (T? /μ) = √ (80/μ) = √4 * √ (20/μ) = 2v?

Since frequency (f) remains the same:
f = v? /λ? = v? /λ?
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3d = 0.6mm

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= 800mm

Path difference is given by

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$\Rightarrow \frac{d y}{D} = (2 n + 1) \frac{λ}{2}$ [for Dark fringe at P]

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$\frac{d y}{D} = \frac{λ}{2}$

$λ = \frac{2 d}{D} y$

$= \frac{2 d}{D} \times \frac{d}{2} [y = \frac{d}{2}, G i v e n$ first dark fringe is observed on the screen directly opposite to one of the slits]

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$\frac{Energy}{Volume} = \frac{{M L}^{2} T^{- 2}}{L^{3}} = ({M L}^{- 1} T^{- 2})$

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10.21 In deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of n $λ$ /a.

Justify this by suitably dividing the slit to bring out the cancellation.

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10.21 In deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of n λ /a. Justify this by suitably dividing the slit to bring out the cancellation.

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10.21 In deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of n $λ$ /a.

Justify this by suitably dividing the slit to bring out the cancellation.