Question

A Plane Wavefront of light of wavelength 5500 A.U. is incident on two slits in a screen perpendicular to the direction of light rays. If the total separation of 10 bright fringes on a screen 2 m away is 2 cm. Find the distance between the slits.​

Answer 1

$\underline{\underline{\maltese\: \: \textbf{\textsf{Answer}}}}$

Given:-

a = 5500 Å,

D = 2 m

Distance between 10 fringes 2 cm

= 0.02 m.

fringe width W 0.02/10

$\sf{⟹0.002 \: m = 2 \times {10}^{ - 3} m}$

To find:-

Distance between slits (d)

Formula:-

$\sf{W = \frac{λD}{d}}$

Calculation: From formula,

$\sf\implies \:2 \times {10}^{ - 3}= \frac{5500 \times {10}^{ - 10} \times 2}{d}$

$\sf\implies \:d = \frac{5.5 \times {10}^{ - 7} \times 2}{2 \times {10}^ { - 3} }$

$\sf\implies \:5.5 \times {10}^{ - 4}m$

Answer 2

Question:-

• A Plane Wavefront of light of wavelength 5500 A.U. is incident on two slits in a screen perpendicular to the direction of light rays. If the total separation of 10 bright fringes on a screen 2 m away is 2 cm. Find the distance between the slits.

To Find:-

• Find the distance between the slits.

Solution:-

Formula to be Used:-

• $\sf \: W = \dfrac{λD}{d}$

According to the Question:-

$\longrightarrow\sf \: 2 \times { 10 }^{ -3 } = \dfrac { 5500 \times { 10 }^{ -10 } \times 2 } { d }$

$\longrightarrow\sf \: d = \dfrac { 5500 \times { 10 }^{ -10 } \times 2 } { 2 \times { 10 }^{ - 3 } }$

$\longrightarrow\sf \: d = 5.5 \times { 10 }^{ -4 } \: m$

Hence ,

• Distance is $\sf \: d = 5.5 \times { 10 }^{ -4 } \: m$