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In Young's double-slit experiment, the y...

In Young's double-slit experiment, the y-coordinate of central maxima and 10th maxima are 2 cm and 5 cm, respectively, When the YDSE apparatus is immersed in a liquid of refractive index 1.5, the corresponding y-coordinates will be

A

2 cm, 7.5 cm

B

3 cm, 6 cm

C

2 cm, 4 cm

D

4/3 cm, 10/3 cm

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To solve the problem, we will follow these steps: ### Step 1: Understand the given data - The y-coordinate of the central maxima (y₀) is given as 2 cm. - The y-coordinate of the 10th maxima (y₁₀) is given as 5 cm. - The refractive index (μ) of the liquid is 1.5. ### Step 2: Determine the fringe width in air The fringe width (β) in Young's double-slit experiment is given by the formula: \[ \beta = \frac{\lambda D}{d} \] where: - λ = wavelength of light - D = distance from the slits to the screen - d = distance between the slits. From the given data, we can express the position of the 10th maxima as: \[ y_{10} = y_0 + 10\beta \] Substituting the known values: \[ 5 = 2 + 10\beta \] \[ 10\beta = 5 - 2 \] \[ 10\beta = 3 \] \[ \beta = \frac{3}{10} \text{ cm} \] ### Step 3: Calculate the new fringe width in the liquid When the apparatus is immersed in a liquid of refractive index μ, the effective wavelength (λ') becomes: \[ \lambda' = \frac{\lambda}{\mu} \] Thus, the new fringe width (β') in the liquid is: \[ \beta' = \frac{\beta}{\mu} \] Substituting the values: \[ \beta' = \frac{\frac{3}{10}}{1.5} = \frac{3}{10} \times \frac{1}{1.5} = \frac{3}{15} = \frac{1}{5} \text{ cm} \] ### Step 4: Calculate the new y-coordinates in the liquid Now, we can find the new y-coordinates for the central maxima (y₀') and the 10th maxima (y₁₀'): 1. For the central maxima: \[ y_0' = y_0 = 2 \text{ cm} \] 2. For the 10th maxima: \[ y_{10}' = y_0' + 10\beta' \] \[ y_{10}' = 2 + 10 \times \frac{1}{5} \] \[ y_{10}' = 2 + 2 = 4 \text{ cm} \] ### Final Results - The new y-coordinate of the central maxima (y₀') is **2 cm**. - The new y-coordinate of the 10th maxima (y₁₀') is **4 cm**. ### Summary of Results - \( y_0' = 2 \text{ cm} \) - \( y_{10}' = 4 \text{ cm} \)
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