Question

A double slit is illuminated by light of wavelength 6000 angstroms. The slits are 0.1 cm apart and the screen is placed 1 m away. Find the angular position of the 10th maximum in radian and the separation between the two adjacent minima. ( No spamming, please)​

Answer 1

Solution

Given

→ d = 0.1 cm = 1 mm

→ D = 1m

→ λ = 6000 A⁰

Formula

→ Angular Position Фₙ = 10th maximum  = (10 λ )/d

→ Angular Position Фₙ  = ( 10 × 6 × 10⁻⁷ )/ 10⁻³ m

→ Angular Position Фₙ = ( 6 × 10⁻⁶)/10⁻³m

→ Angular Position Фₙ  = 6 × 10⁻³ Radian

To Separation between  two adjacent minima we have to find fringe width

→ Fringe width ( β) = λD/d

Put the value on formula

→ Fringe width ( β) = λD/d

→Fringe width ( β) = (6 × 10⁻⁷ × 1 )/10 ⁻³

→ Fringe width ( β) = 6 × 10⁻⁴ m

Answer

i)Angular Position Фₙ  = 6 × 10⁻³ Radian

ii)  Fringe width ( β) = 6 × 10⁻⁴ m

Answer 2

$\sf\fcolorbox{gray}{white}{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:Answer\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}$

$\bold\pink{Given}$

$\sf\color{navy}{ d = 0.1 cm = 1 mm}$

$\sf\color{navy}{ D = 1m}$

$\sf\color{navy}{ λ = 6000 A⁰}$

$\bold\pink{Solution}$

$\sf\color{navy}{ Angular\: Position \:Ф_n= 10th\: maximum = (\frac {10 λ}{d})}$

$\sf\color{navy}{ Angular\: Position\: Ф_n = (\frac{ 10 × 6 × 10^{-7}}{10^{-3}m})}$

$\sf\color{navy}{Angular\:Position \:Ф_n \:= (\frac {6 \times 10^{-6}}{10^{-3}m})}$

$\sf\color{navy}{Angular\: Position \:Ф_n \:= 6 \times 10^{-3} \:Radian}$

$\sf\color{blue}{To\: Separation\: between\: two\: adjacent\: minima\: we}$ $\sf\color{blue}{have\: to \:find\: fringe \:width}$

$\sf\color{navy}{Fringe\: width\: ( β) = \frac {λD}{d}}$

$\sf\color{blue}{Substituting \:the\: valuse\: in\: formula}$

$\sf\color{navy}{Fringe\: width\: ( β) = \frac{λD}{d}}$

$\sf\color{navy}{Fringe\: width\: ( β) = \frac{(6 × 10^{-7} \times 1 )}{10^{-3}}}$

$\sf\color{navy}{Fringe \:width\: ( β) = 6 × 10^{-4}m}$

$\sf\color{blue}{Hence,}$$\sf\color{blue}{Angular\: Position\: Ф_n = 6 \times 10^{-3} \:Radian}$

$\sf\color{blue}{Fringe \:width \:( β) = 6 \times 10^{-4}\:m=0.0006\:m}$