Name: Chromatic Aberration
Uploaded: 2019-07-19
Duration: 5 min 45 s
Description: Do you know what chromatic aberration in lenses is? How can we reduce this? Let's dive into the concept behind it and learn to avoid it in the future.

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

15

cm. Calculate the chromatic aberration between extreme colours.

Accepted Answer

Given that $n_{V} = 1.66, n_{R} = 1.60, R_{1} = 10 cm, R_{2} = - 15 cm$ .

Chromatic aberration between extreme colours $= f_{R} - f_{V}$

Using Lens maker's formula, $\frac{1}{f} = (n - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

For violet,

$\frac{1}{f_{V}} = (1.66 - 1) (\frac{1}{10} - (\frac{1}{- 15})) ∴ \frac{1}{f_{V}} = (0.66) (\frac{1}{10} + \frac{1}{15}) ∴ \frac{1}{f_{V}} = (0.66) (\frac{25}{150}) ∴ \frac{1}{f_{V}} = (0.66) (\frac{1}{6}) ∴ f_{V} = \frac{6}{0.66} ∴ f_{V} = \frac{100}{11}$

For red,

$\frac{1}{f_{R}} = (1.60 - 1) (\frac{1}{10} - (\frac{1}{- 15})) ∴ \frac{1}{f_{R}} = (0.60) (\frac{1}{10} + \frac{1}{15}) ∴ \frac{1}{f_{R}} = (0.60) (\frac{25}{150}) ∴ \frac{1}{f_{R}} = (0.60) (\frac{1}{6}) ∴ f_{R} = \frac{6}{0.60} ∴ f_{R} = 10$

Chromatic aberration $= f_{R} - f_{V} = 10 - \frac{100}{11} = \frac{110 - 100}{11} = \frac{10}{11} cm$

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 $15$ cm. Calculate the chromatic aberration between extreme colours.

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