# In figure, the optical fiber is l = 2 m long and has a diameter of $d=20\mu m.$ If a ray of light is incident on one end of the fiber at angle $\theta}_{1}={40}^{\circ$ , the number of reflections it makes before emerging form the other end is close to : (refractive index of fiber is 1.31 and ${\mathrm{sin}40}^{\circ}=0.64$)

66000

45000

57000

55000

## The correct Answer is:C

## $1{\mathrm{sin}40}^{\circ}=1.31\mathrm{sin}r$

$0.64=1.31\mathrm{sin}r$

$\mathrm{sin}r-\frac{0.64}{1.31}=0.49\approx 0.5\Rightarrow r=30$

So $\theta ={60}^{\circ}\therefore \theta >c$

$\therefore$ T.I.R. at other surface

$\mathrm{tan}r=\frac{20\mu m}{x}\Rightarrow x=20\sqrt{3}\mu m$

$n=\frac{2m}{20\sqrt{3}\mu m}\Rightarrow n=\frac{{10}^{5}}{\sqrt{3}}\Rightarrow n=57803$

### Similar Questions

Two plane mirrors each 1.6 m long, are facing each other. The distance between the mirrors is

20 cm. A light incident on one end of one of the mirrors at an angle of incidence of 30∘. How many times is the ray reflected before it reaches the other end?View SolutionA ray of light is incident on a glass plate of refractive index 1.54. If the reflected ray is completely plane polarised, find (i) angle of incidence (ii) angle of refraction and (iii) crictical angle. Given tan57∘=1.54 and sin40.5∘=0.6493.

View Solution

### Knowledge Check

- Question 1 - Select One
## Two parallel plane mirrors M1andM2 have a length of 2 m each and are 10 mm apart. A ray of light is incident on one end of mirror M2 at an angle of 30∘. The number of reflections light undergoes before reaching the other end is –

A346B134C80D173 - Question 2 - Select One
## Two plane mirrors M1 and M2 each have length 1m and are separated by 1cm. A ray of light is incident on one end of mirror M1 at angle 45∘. How many reflections the ray will have before going from the other end?

A50B51C100D101 - Question 3 - Select One
## The mirrors each 1.6 m long are facing each other, The distance between the mirrors is 20 cm. A light ray is incident on one end of the mirror at an angle of incidence of 30∘ . How many times is the ray reflected before it reaches the other end?

AThere are 15 reflections counting the first oneBThere are 13 reflections counting the first oneCThere are 12 reflections counting the first oneDNone of the above

An optical fiber has index of refraction n=1.40 and diameter d=100μm. It is surrounded by air. Light is sent into the fiber along the axis as shown in figure. If smallest outside radius R permitted for a bend in the fiber for no light to escape is given by 50x(inμm) fill value of x.

View SolutionAn optical fiber has index of refraction n=1.40 and diameter d=100μm. It is surrounded by air. Light is sent into the fiber along the axis as shown in figure. If smallest outside raidus R permitted for a bend in the fiber for no light to escape is given by 50 x (in μ m) fill value of x.

View SolutionThe figure given below shows a solid glass block of refractive index 1.5. the lower surface of the block is silvered and behaves as a reflecting mirror. A white light ray AB incidents on the glass block at angle of incidence 40∘. Copy the diagram and trace the path of reflected and refracted rays from upper and lower surfaces of the block. (Take sin40∘=0.64andsin26∘=0.43)

View SolutionAn equiconvex lens has its two surfaces of radius of curvature R=10cm. Thickness of the lens at its centre is 2 cm. A light ray is incident making an angle of 2° with the optic axis of the lens. Find the angle that the emergent ray will make with the optic axis. The refractive index of all media is as marked in the Figure.

View SolutionWhat is the least radius through which an optical fiber of core diameter 0.05 mm may be bent (as shown in figure) without serious loss of light? The refractive index of the core is 1.6 and that of cladding is 1.5.

View Solution