Question

Refractive index of a flint glass varies from 1.60 to 1.66 for visible range. Radii of curvature of a thin convex lens are 10 cm and 12 cm. The chromatic aberration between extreme colours is ____________.

Options

• 1.33 cm

• 0.67 cm

• 1.5 cm

• 0.83 cm

Answer 1

Refractive index of a flint glass varies from 1.60 to 1.66 for visible range. Radii of curvature of a thin convex lens are 10 cm and 12 cm. The chromatic aberration between extreme colours is 0.83 cm.

Explanation:

Given are the refractive indices for extreme colours. As, n_R < n_V
n_R = 1.60 and n_V = 1.66
For convex lens,
R₁ = 10 cm and R₂ = – 12 cm
` therefore (1/"R"_1-1/"R"_2)=(1/10-1/-12)=11/60`
For red colour,
`1/"f"_"R"=("n"_"R"-1)(1/"R"_1-1/"R"_2)`
`= (1.60 − 1) 11/60`
`= 0.11`

`therefore "f"_"R" = 9.09  "cm"`
Similarly, for violet colour,
`1/"f"_"V"=("n"_"V"-1)(1/"R"_1-1/"R"_2)`
`= (1.66 − 1) 11/60`
`= 0.121`
`therefore "f"_"V" = 8.26  "cm"`
∴ Longitudinal chromatic aberration
`="f"_"V" - "F"_"R" = 0/09 - 8.26 = 0.83 "cm"`