Red light of wavelength 6400 A ∘ in air has wavelength 4000 A ∘ in glass. If the wavelength of violet light in air is 4400 A ∘ , what is its wavelength in glass? (Hint: Assume that μ r and μ v are approximately equal)

Given, λ r ( a i r ) = 6400 A ∘ , λ r ( g l a s s ) = 4000 A ∘ , λ v ( a i r ) = 4400 A ∘ and λ v ( g l a s s ) = ? Refractive index is given by, μ = λ a i r λ g l a s s From the given hint, μ r = μ v λ r ( a i r ) λ r ( g l a s s ) = λ v ( a i r ) λ v ( g l a s s ) 6400 4000 = 4400 λ v ( g l a s s ) λ v ( g l a s s ) = 40 × 4400 64 λ v ( g l a s s ) = 2750 A ∘ Therefore, the wavelength of violet light in glass medium is 2750 A ∘ .

If the difference in velocities of light in glass and water is 0 . 25 × 10 8 m / s , find the velocity of light in air. (given: μ g = 1 . 5 , μ w = 4 / 3 )

Given, v w - v g = 0 . 25 × 10 8 m / s μ g = 1 . 5 μ w = 4 3 c = ? We know that refractive index is given by, μ = c v ∴ v = c μ From the question, v w - v g = 0 . 25 × 10 8 c μ w - c μ g = 0 . 25 × 10 8 c 1 μ w - 1 μ g = 0 . 25 × 10 8 c 3 4 - 2 3 = 0 . 25 × 10 8 c × 1 12 = 0 . 25 × 10 8 c = 0 . 25 × 10 8 × 12 c = 3 × 10 8 m / s Therefore, the the velocity of light in air is 3 × 10 8 m / s

A small angled prism of 4 ° deviates a ray through 2 . 48 ° . Find the refractive Index of the prism.

It is given that the prism under consideration is a thin prism. Also, The angle of prism, A = 4 ° Angle of deviation, δ = 2 . 48 ° Let n be the refractive index of the prism. We know that for a thin prism, δ = A n - 1 ⇒ n = δ A + 1 ⇒ n = 1 . 62