White light is passed through a double slit and interference is observed on a screen 1.5 m away. The separation between the slits is 0.3 mm. The first violet and red fringes are formed 2,0 mm and 3.5 mm away from the central white fringes. The difference in wavelengths of red and violet light is nm.

Question

White light is passed through a double slit and interference is observed on a screen 1.5 m away. The separation between the slits is 0.3 mm. The first violet and red fringes are formed 2,0 mm and 3.5 mm away from the central white fringes. The difference in wavelengths of red and violet light is nm. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Position of bright fringe y = n ( D λ/ d ) y 1 of red =( D λ r / d )=3.5 mm λ r =3.5 × 10-3 ( d / D ) Similarly λv=2 × 10-3 ( d / D ) λ r -λ v =(1.5 × 10-3)((0.3 × 10-3/1.5)) =3 × 10-7=300 nm

Position of bright fringe y=ndDλ​ y1​ of red =dDλr​​=3.5mm λr​=3.5×10−3Dd​ Similarly λv​=2×10−3Dd​ λr​−λv​=(1.5×10−3)(1.50.3×10−3​) =3×10−7=300nm