Question

A plano-convex lens of radius 1.0 m is placed on an optically flat glass plate and is illuminated by an extended monochromatic source. Assume that the point of contact is perfect. The diameters of the 10th and 5th dark rings in the reflected light are 4.50 × 10−3m and 3.36 × 10−3m. Next, the space between the lens and the glass plate is filled with a liquid. The diameter of the 5th ring changes to 3.0×10−3m. Calculate the refractive index of the liquid when the ring is (i) dark, and (ii) bright, if the wavelength of light is 589 nm.

Answer 1

Answer on Question #65171, Physics / Optics

A plano-convex lens of radius $1.0\,\mathrm{m}$ is placed on an optically flat glass plate and is illuminated by an extended monochromatic source. Assume that the point of contact is perfect. The diameters of the 10th and 5th dark rings in the reflected light are $4.50 \times 10^{-3}\,\mathrm{m}$ and $3.36 \times 10^{-3}\,\mathrm{m}$. Next, the space between the lens and the glass plate is filled with a liquid. The diameter of the 5th ring changes to $3.0 \times 10^{-3}\,\mathrm{m}$. Calculate the refractive index of the liquid when the ring is (i) dark, and (ii) bright, if the wavelength of light is $589\,\mathrm{nm}$.

Find: $n_{\mathrm{dark}} - ?n_{\mathrm{bright}} - ?$

Given:

$$\begin{array}{l} R = 1.0\,\mathrm{m} \\ r_5 = 1.5 \times 10^{-3}\,\mathrm{m} \\ \lambda = 589 \times 10^{-9}\,\mathrm{m} \\ \end{array}$$

Solution:

For dark ring: $r_5 = \sqrt{\frac{kR\lambda}{n}}$ (1), where $k = 5$

Of (1) $\Rightarrow n = \frac{kR\lambda}{r_5^2}$ (2)

Of (2) $\Rightarrow n = 1.3089$

For bright ring: $r_5 = \sqrt{\frac{(2k - 1)R\lambda}{2n}}$ (3), where $k = 5$

Of (3) $\Rightarrow n = \frac{(2k - 1)R\lambda}{2r_5^2}$ (4)

Of (4) $\Rightarrow n = 1.1780$

Answer:

(i) 1.3089

(ii) 1.1780

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