Question

Find the angular separation between the consecutive bright fringes in a Young's double slit experiment with blue-green light of wavelength 500 nm. The separation between the slits is 2·0×10-3 m.

Answer 1

The angular separation between the consecutive bright fringes in the given Young's double slit experiment = 0.1414 degree

λ = wavelength of the light = 500 nm = 500 × 10^-9 m

d = separation between the slits = 2 × 10^-3 m

Θ = angular separation between the consecutive bright fringes in the Young's double slit experiment

Θ = β/D = λD/dD = λ/d = wavelength of light / separation between the slits

Θ = λ/d = 5 × 10^-7 / 2 × 10^-3

= 2.5 × 10^-4 radian

= 0.1414 degree

The angular separation is equal to 0.1414 degrees

Answer 2

The angular separation between the consecutive bright fringes is $0.014^{\circ}$

Explanation:

Step 1:

Given data,

Blue-green light Wavelength  $=\lambda=500 \times 10^{-9} \mathrm{m}$  

Divide between $2 \text { slits }=\mathrm{d}=2 \times 10^{-3} \mathrm{m}$

Let the angular separation between the bright fringes be consecutive θ.

Step 2:

Formula :

Angular seperation $=\theta=\frac{\beta}{D}$

$=\frac{\lambda D}{d D}$

$=\frac{\lambda}{\mathrm{d}}$

Step 3:

$\theta=\frac{\beta}{D}=\frac{500 \times 10^{-9}}{2 \times 10^{-3}}$

$=250 \times 10^{-6}$

$=25 \times 10^{-5} \text { radian }$

$=0.014^{\circ}$

The angular separation between the consequent bright fringes is thus $0.014$degree.