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’.
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(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,
$\text {Speed of light in vacuum (c)} = \frac {\text {Distance travelled by light in vacuum}}{\text {Time taken by light in vacuum}}= \frac {10\text x}{\text t_1}$
and
$\text {Speed of light in diamond (v)} = \frac {\text {Distance travelled by light in diamond}}{\text {Time taken by light in diamond}}= \frac {\text x}{\text t_2}$
then,
$$\begin{aligned}\text {The refractive index of diamond} = \frac{\text{Speed of light in vacuum (c)}}{\text {speed of light in diamond (v)}}= \frac{\frac {10\text x}{\text t_1}}{\frac {\text x}{\text t_2}} \\[1em] =\frac{10 \text t_2}{\text t_1}\end{aligned}$$