A double-slit is illuminated by light of wavelength 6000A. The slits are 0.1 cm apart and the screen is placed 1 m away. Calculate (i) angular position of 10 th maximum in radian (ii) separation of two adjacent minima.

Solution

Given ,
Wavelength of the light source,

λ

= 6000

\overset{o}{A}

Distance between the slits, d = 0.1 cm = 0.1

\times 10^{- 2} m

Distance between the screen and the slit, D = 1 m

(i) Angular position of nth maximum is given by,

θ_{n} = \frac{x_{n}}{D} = \frac{nDλ}{dD} = \frac{nλ}{d} ∴ χ_{n} = \frac{n D λ}{d}

Angular position of 10th maximum,

θ_{10} = \frac{10 \times 6000 \times 10^{- 10}}{0.1 \times 10^{- 2}} = 6 \times 10^{- 3} radian

(ii) Separation between two adjacent minima

i.e., fringe width,

ω = \frac{Dλ}{d}

\Rightarrow

ω = \frac{1 \times 6000 \times 10^{- 10}}{10^{- 3}}

= 6 \times 10^{- 4} m = 0.6 mm .

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