Light travels a distance of ‘10x’ units in time ‘t₁’ in vacuum and it travels a distance of ‘x’ units in time ‘t₂’ in a denser medium. Using this information answer the question that follows :

(a) ‘Light covers a distance of ‘20x’ units in time ‘t₁’ in diamond.’ State true or false.

(b) Calculate the refractive index of the medium in terms of ‘t₁’ and ‘t₂’.

(a) False because speed of light in vacuum is highest and diamond is a denser medium so speed of light will be lower and hence, it can not travel a distance 20x in diamond which is two times of distance travelled by light in vacuum.

(b) Given,

Distance travelled by light in vacuum = 10x

Time taken by light in vacuum = t₁

Distance travelled by light in the medium = x

Time taken by light in diamond = t₂

As,

$\text {Speed of light in vacuum (c)} = \dfrac {\text {Distance travelled by light in vacuum}}{\text {Time taken by light in vacuum}}= \dfrac {10\text x}{\text t_1}$

and

$\text {Speed of light in diamond (v)} = \dfrac {\text {Distance travelled by light in diamond}}{\text {Time taken by light in diamond}}= \dfrac {\text x}{\text t_2}$

then,

$\text {The refractive index of diamond} = \dfrac{\text{Speed of light in vacuum (c)}}{\text {speed of light in diamond (v)}}= \dfrac{\dfrac {10\text x}{\text t$1}}{\dfrac {\text x}{\text t2}} \\[1em] =\dfrac{10 \text t2}{\text t1}