Answer

Verified

45.6k+ views

**Hint:**The phenomenon of Total internal reflection only occurs when the angle of incidence is greater than the critical angle. These types of questions can be solved by first finding the critical angle and then using Snell’s law to obtain the angle of incidence.

**Formula Used:**

Snell’s law is used to obtain the angle of incidence. Mathematically it is given as follows:

$ \mu = \dfrac{{\sin i}}{{\sin r}} $

**Complete step by step solution:**

Refractive index of quartz filaments is 1.70 and the refractive index of coating material is 1.45. Thus, total refractive index is given by

$ \mu = \dfrac{{1.70}}{{1.45}} = 1.17 $

Now we know that the sine of a critical angle is the inverse of the refractive index of the medium. Thus,

$ \sin {i_c} = \dfrac{1}{\mu } = \dfrac{1}{{1.17}} = 0.856 $

Now we can find the value of critical angle.

$ {i_c} = {\sin ^{ - 1}}0.856 = 58.5^\circ $

We know that for total internal reflection to take place, the value of angle of incidence should be more than that of the critical angle. Thus,

$ {i'} > 58.5^\circ $

So, angle of refraction is given as:

$ r = 90 - {r'} $

Here r is the angle of refraction of the laser beam and r’ is the angle of refraction inside the fibre. Thus,

$

r < {90^ \circ } - 58.5^\circ \\

\Rightarrow r < 31.5^\circ $

Now we can use Snell’s law to obtain an angle of incidence. According to Snell’s law:

$\dfrac{{\sin i}}{{\sin r}} = {}_g^a\mu $

Putting the respective values in the above equation, we get:

$\dfrac{{\sin i}}{{\sin 31.5^\circ }} = 1.70$

Now, we can easily solve the equation.

$

\sin i = 1.70 \times \sin 31.5^\circ \\

\Rightarrow \sin i = 1.70 \times 0.524 = 0.89$

Now we can easily find the value of angle of incidence.

$ i = {\sin ^{ - 1}}0.89 = 62.6^\circ $

**Thus, the value of angle of incidence can be anywhere between 0° to 62.6°. Hence the correct option is option (B).**

**Note:**Usually students get confused when there are multiple angles of reflections and angle of incidences. It is important to use the value of angle of incidence and reflection correctly. Always remember to match the values according to the value of the refractive index.

Recently Updated Pages

To get a maximum current in an external resistance class 1 physics JEE_Main

f a body travels with constant acceleration which of class 1 physics JEE_Main

A hollow sphere of mass M and radius R is rotating class 1 physics JEE_Main

If the beams of electrons and protons move parallel class 1 physics JEE_Main

Two radioactive nuclei P and Q in a given sample decay class 1 physics JEE_Main

silver wire has diameter 04mm and resistivity 16 times class 12 physics JEE_Main

Other Pages

Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main

Explain the construction and working of a GeigerMuller class 12 physics JEE_Main

Which of the following is not a redox reaction A CaCO3 class 11 chemistry JEE_Main

Electric field due to uniformly charged sphere class 12 physics JEE_Main

when an object Is placed at a distance of 60 cm from class 12 physics JEE_Main

Two identical particles each having a charge of 20 class 12 physics JEE_Main