In a Young's double slit experiment, slits are separated by \(0.5\ mm\), and the screen is placed \(150\ cm\) away. A beam of light consisting of two wavelengths, \(650\ nm\) and \(520\ nm\), is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is...... \(mm\)

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Verified Solution

Answer & Solution

Correct Answer

(B) \(7.8\)

Detailed explanation

For common maxima, \(n_{1} \lambda_{1}=n_{2} \lambda_{2}\)

\(\Rightarrow \quad \frac{n_{1}}{n_{2}}=\frac{\lambda_{2}}{\lambda_{1}}=\frac{520 \times 10^{-9}}{650 \times 10^{-9}}=\frac{4}{5}\)

For \(\lambda_{1}\)

\(y=\frac{n_{1} \lambda_{1} D}{d}, \lambda_{1}=650\, \mathrm{nm}\)

\(y=\frac{4 \times 650 \times 10^{-9} \times 1.5}{0.5 \times 10^{-3}} \quad\) or, \(y=7.8\,\mathrm{mn}\)

Same subject

List - I	List - II
(A) Heat capacity of body	\(\text{(I) } \mathrm{J} \mathrm{kg}^{-1}\)
(B) Specific heat capacity of body	\(\text{(II) } \mathrm{JK}^{-1}\)
(C) Latent heat	\(\text{(III) } \mathrm{J} \mathrm{kg}^{-1} \mathrm{~K}^{-1}\)
(D) Thermal conductivity	\(\text{(IV) } \mathrm{Jm}^{-1} \mathrm{~K}^{-1} \mathrm{~s}^{-1}\)

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