Draw a plot showing the variation of power of a lens with the wavelength of the incident light. A diverging lens of refractive index $1.5$ and of focal length $20\ \mathrm{cm}$ in air has the same radii of curvature for both sides. If it is immersed in a liquid of refractive index $1.7$, calculate the focal length of the lens in the liquid.

Power decreases as wavelength increases (since $\mu$ decreases with $\lambda$). In the liquid the lens becomes converging with $f_{\text{liq}}=+85\ \mathrm{cm}$.

CBSE Class 12 · 2008 · Geometrical OpticsShort Answer

WhatsApp Email

Draw a plot showing the variation of power of a lens with the wavelength of the incident light. A diverging lens of refractive index

1.5

and of focal length

20 cm

in air has the same radii of curvature for both sides. If it is immersed in a liquid of refractive index

1.7

, calculate the focal length of the lens in the liquid.

Solution

Power

P = (μ - 1) (\frac{1}{R _{1}} - \frac{1}{R _{2}})

and

μ

decreases with increasing

λ

, so the power–wavelength graph falls as

λ

increases.
Taking

K = (\frac{1}{R _{1}} - \frac{1}{R _{2}})

: in air

\frac{1}{- 20} = (1.5 - 1) K \Rightarrow K = - 0.1 c m^{- 1}

.
In the liquid:

\frac{1}{f _{liq}} = (\frac{1.5}{1.7} - 1) K = (- 0.1176) (- 0.1) = 0.01176 c m^{- 1}

f_{liq} = + 85 cm (converging)

The nature reverses because

μ_{liquid} > μ_{glass}

CBSE Class 12 Board · 2008 · Subjective

Practise more: all CBSE board PYQs on Geometrical Optics →

CBSE Class 12 · 2008 · Geometrical OpticsShort Answer

Solution

More board questions on Geometrical Optics