Physics, asked by sureahmagadigowda, 11 months ago

slit for a


In Young's double slit experiment the slit seperation
is 1mm and the screen is 1m from the slit for a
monochromatic light of wavelength 500nm,the
distance of 3rd
minima is​

Answers

Answered by Anonymous
92

In Young's double-slit experiment the slit separation is 1mm.

(silt separation = d = 1 mm)

{ 1 mm = 1 × 10-³ m }

Also given that, separation from the screen from the slit is 1 m.

(D = 1 m)

Monochromatic light of wavelength 500 nm.

(\sf{\lambda} = 500 nm)

{ 500 nm = 500 × 10^(-9) m }

Now,

\sf{x_n\:=\:\dfrac{(2n-1)\lambda D}{2d}}

We have to find the distance of 3rd minima.

(n = 3)

\sf{x_3\:=\:\dfrac{(2 \times 3-1)\lambda D}{2d}}

Substitute the known values

\sf{x_3\:=\:\dfrac{(2 \times 3-1)500 \times 10^{-9} \times 1}{2 \times 10^{-3}}}

\sf{x_3\:=\:\dfrac{(6-1)500 \times 10^{-9} \times 1}{2 \times1 \times 10^{-3}}}

\sf{x_3\:=\:\dfrac{(5)500 \times 10^{-9} \times 1}{2 \times 10^{-3}}}

\sf{x_3\:=\:\dfrac{2500 \times 10^{-9} \times 1}{2 \times 10^{-3}}}

\sf{x_3\:=\:\dfrac{2500 \times 10^{-6} \times 1}{2}}

\sf{x_3\:=\:1250 \times 10^{-6}}

\sf{x_3\:=\:1.25 \times 10^{-3} m}

OR

\sf{x_3\:=\:1.25 mm}


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Answered by AdorableMe
123

Given :-

• In Young's double slit experiment the slit separation  is 1 mm.

• The screen is 1 m from the slit for a  monochromatic light of wavelength 500 nm.

To find :-

The distance of the third minima(\tt{x_3}).

Solution :-

Silt separation = d = 1 mm      (given)

D = 1 m                                     (given)

Wavelength given 500 nm = \sf{500 * 10^-^9} m.

• d = 1 nm = \sf{1 * 10^-^3\ m}

• D = 1 m

• n = 3

We know,

\bold{\sf{x_3 = \frac{[(2n-1) \lambda D]}{2d} }}

\tt{\implies x_3=\frac{(2*3-1) \lambda D}{2d} }\\\\\tt{\implies x_3=\frac{(6-1)*500*10^-^1^9*1}{2*10^-^3*1} }\\\\\tt{\implies x_3=\frac{(5)500*10^-^1^9}{2*10^-^3} }\\\\\tt{\implies x_3=\frac{2500*10^-^1^9}{2*10^-^3} }\\\\\tt{\implies x_3=\frac{2500*10^-^6}{2} }\\\\\tt{\implies x_3=1.25*10^-^3\ m}\\\\\huge\boxed{\tt{\implies x_3=1.25\ mm}}

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