Laser light of wavelength 630 nm incident on a pair of slits produces an interference pattern in which the bright fringes are separated by 8.1 mm. A second light produces an interference pattern in which the fringes are separated by 7.2 mm. The wavelength of the second light is

Question

Laser light of wavelength 630 nm incident on a pair of slits produces an interference pattern in which the bright fringes are separated by 8.1 mm. A second light produces an interference pattern in which the fringes are separated by 7.2 mm. The wavelength of the second light is (A) 420 nm (B) 560 nm (C) 810 nm (D) 980 nm

Tardigrade Admin · Accepted Answer

Here λ1 = 630 nm, Î²1 = 8.1 mm, Î²2 = 7.2 mm Fringe width, β=(Dλ/d) For constant D and d, Î² â λ ∴ (β2/β1)=(λ2/λ1) ∴ λ2=(β2/β1)×λ1=(7.2 mm/8.1 mm)×630 nm=560 nm.

Q. Laser light of wavelength 630 nm incident on a pair of slits produces an interference pattern in which the bright fringes are separated by 8.1 mm. A second light produces an interference pattern in which the fringes are separated by $7.2 mm$ . The wavelength of the second light is

$420 nm$

$560 nm$

$810 nm$

$980 nm$

Here $λ_{1} = 630 nm, β_{1} = 8.1 mm, β_{2} = 7.2 mm$
Fringe width, $β = \frac{D λ}{d}$
For constant $D$ and $d, β \propto λ$
$∴ \frac{β _{2}}{β _{1}} = \frac{λ _{2}}{λ _{1}}$
$∴ λ_{2} = \frac{β _{2}}{β _{1}} \times λ_{1} = \frac{7.2 mm}{8.1 mm} \times 630 nm = 560 nm .$

Q. Laser light of wavelength 630 nm incident on a pair of slits produces an interference pattern in which the bright fringes are separated by 8.1 mm. A second light produces an interference pattern in which the fringes are separated by 7.2mm. The wavelength of the second light is

420nm

560nm

810nm

980nm