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Engineering
2 weeks ago

# MHT-CET When the same monochromatic ray of light travels through water, the number of waves in glass slab of thickness 6 cm is same as in

water column of height  7 cm. If refractive index of water is

1. 1.269

2. 1.286

3. 1.259

4. 1.310

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A Abhishek Sahu
Answered 1 week, 6 days ago

It is given that wave number in 6cm of glass is the same as the wave number in water with height 7 cm.

Let $\lambda _{g}$ is wavelength of light in glass and $\lambda _{w}$  is wavelength of light in water.

According to question, $\frac{6}{\lambda _{g}} = \frac{7}{\lambda _{w}} \Rightarrow \frac{\lambda _{w}}{\lambda _{g}} = \frac{7}{6}$

Also we know that relation between refractive index and wavelength, $\frac{\mu _{g}}{\mu _{w}} = \frac{\lambda _{w}}{\lambda _{g}}$

Putting values, $\frac{1.5}{\mu _{w}} = \frac{7}{6} \Rightarrow \mu _{w} = 1.286$

Option (2) is correct

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