Question

the optical path of a ray of light of a given wavelength travelling a distance of 3 cm in flint glass having refractive index 1.6 is same as that on travelling a distance x cm through a medium having refractive index 1.25 Determine the value of x.
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Answer 1

Given that,

The wavelength travelling a distance of 3 cm in flint glass.

Refractive index of flint glass = 1.6

Refractive index of another medium = 1.25

We know that,

Refractive index is inversely proportional to the wavelength.

$\mu\propto\dfrac{1}{\lambda}$

We need to calculate the value of x

Using formula of refractive index

$\mu=\dfrac{v}{\lambda}$....(I)

We know that,

$v=\dfrac{d}{t}$

Put the value of v in equation (I)

$\mu=\dfrac{d}{\lambda t}$

For both medium,

$\dfrac{\mu_{f}}{\mu_{m}}=\dfrac{d}{x}$

Put the value into the formula

$\dfrac{1.6}{1.25}=\dfrac{3}{x}$

$x=\dfrac{1.25\times3}{1.6}$

$x=2.34\ cm$

Hence, The value of x is 2.34 cm

Answer 2

Answer: given:the distance travelled by wavelength in flint glass is 3 cm

The refractive index of Flint glass is 1.6

The refractive index of another medium is 1.25

Solution: 1.6/1.25=x/3

Therefore x=(3*1.6)/1.25

x=96/25

x=3.84cm

Hope it helps you