(i) Monochromatic light of wavelength 589 nm is incident from air on a

1.	(i) Monochromatic light of wavelength 589 nm is incident from air on a water surface. If μ for water is 1.33, find the wavelength, frequency and speed of the refracted light.(ii) A double convex lens is made of a glass of refractive index 1.55, with both faces of the same radius of curvature. Find the radius of curvature required, if the focal length is 20 cm.
Answer» (i) \(λ=\frac{589\,nm}{1.33}=442.8\,nm\) Frequency \(v=\frac{3\times10^8ms^{-1}}{589\,nm}=5.09\times10^{14}Hz\) Speed \(v=\frac{3\times10^8}{1.33}m/s=2.25\times10^8m/s\) (ii) \(\frac{1}{f}=[\frac{μ_{ga}}{u_1}-1][\frac{1}{R_1}-\frac{1}{R_2}]\) \(∴\frac{1}{20}=[\frac{1.55}{1}-1]\frac{2}{R}\) ∴ R = (20 × 1.10) cm = 22 cm

(i) Monochromatic light of wavelength 589 nm is incident from air on a water surface. If μ for water is 1.33, find the wavelength, frequency and speed of the refracted light.(ii) A double convex lens is made of a glass of refractive index 1.55, with both faces of the same radius of curvature. Find the radius of curvature required, if the focal length is 20 cm.

Answer»

(i) \(λ=\frac{589\,nm}{1.33}=442.8\,nm\)

Frequency \(v=\frac{3\times10^8ms^{-1}}{589\,nm}=5.09\times10^{14}Hz\)

Speed \(v=\frac{3\times10^8}{1.33}m/s=2.25\times10^8m/s\)

(ii) \(\frac{1}{f}=[\frac{μ_{ga}}{u_1}-1][\frac{1}{R_1}-\frac{1}{R_2}]\)

\(∴\frac{1}{20}=[\frac{1.55}{1}-1]\frac{2}{R}\)

∴ R = (20 × 1.10) cm = 22 cm