Home
Class 12
PHYSICS
A ray of light from a denser medium stri...


A ray of light from a denser medium strike a rarer medium at an angle of incidence I (see Fig). The reflected and refracted rays make as angle of 90degrees with each other. The angles of reflection and refraction are r and `r` The critical angle is

A

`sin ^(-1)` (tan r)

B

`sin ^(-1)` (cot i)

C

`tan^(-1)` (Sin r)

D

`tan^(-1)` (sin i)

Text Solution

Verified by Experts

The correct Answer is:
A
Applying SneH.s Law for refraction`sini/sinr = n_(2)/n_(1)` ….(i)
From the given condition, r + `r^(.)` = 9
implies sin `r^(.)` = cos r ….....(2)
Solution of (1) and. (2) yields`sini/cosr=n_(2)/n_(r)` …...(3)
According to the Law for refraction,
i = r .....(4)
Using (3) and (4) we obtain
`sini/cosi=n_(2)/n_(1)` .....(5)
Also sin`theta_(c)=n_(2)/n_(1)`,Using(5)We obtain`theta_(c)=sin_(-1)`(tani)=`sin_(-1)`(tanr)
Hence (A) is correct.
Promotional Banner

Topper's Solved these Questions

  • OPTICS

    FIITJEE|Exercise Comprehension-1(prob)|3 Videos

  • OPTICS

    FIITJEE|Exercise Comprehension-2(prob)|3 Videos

  • OPTICS

    FIITJEE|Exercise SOLVED PROBLEMS (SUBJECTIVE)|18 Videos

  • MODERN PHYSICS

    FIITJEE|Exercise Numerical based questions|5 Videos

  • PHYSICS PART-III

    FIITJEE|Exercise NUMERICAL BASED QUESTIONS DECIMAL TYPE|11 Videos

Similar Questions

Explore conceptually related problems

A ray of light from a denser medium strikes a rarer medium at an angle of incidence I (see figure ). The reflected and refracted rays make an angle of 90^(@) with each other. The angles of reflection and refraction are r and r^() . The critical angle is

A ray of light from a denser medium strikes a rarer medium at angle of incidence i . The refrected and the refracted rays make an angle of 90^@ with each other. The angles of reflection and refraction are r and r^' respectively. The critical angle is (i) sin^-1(tanr) (ii) sin^-1(tani) (iii) sin^-1(tanr) (iv) tan^-1(tani)

A ray of light passes from a denser medium to a rarer medium at an angle of incidence i. The reflected and refracted rays make an angle of 90^@ with each other. The angle of reflection and refraction are resepectively r and r'. The critical angle is given by :

A ray of light from a denser medium strikes a rarer medium at an angle of incidenc i. The reflected and refracted rays make an angle of pi//2 with each other. If the angles of reflection and refraction are r and r^(') , then the criticall angle will be

A ray of light from a denser medium strikes a rarer medium at an angle of incidence i. if the reflected and the refracted rays are mutually perpendicular to each other, what is the value of the critical angle ?

If a ray of light in a denser medium strikes a rarer medium at an angle of incidence i, the angles of reflection and refraction are respectively, r and r' If the reflected and refraction rays are at right angles to each other, the critical angle for the given pair of media is

A ray of light from a denser medium strikes a rarer medium at an angle of incidence i = tan^( -1)(1//2) . If the reflected and the refracted rays are mutually perpendicular to each-other, what is the value of the critical angle in degree?

A ray of light from a rarer medium strikes a denser medium at angle of incidence 60°. The reflected and refracted rays are perpendicular to each other. The refractive index of denser medium and angle of deviation respectively are

A ray of light is incident at an angle i from denser to rare medium. The reflected and the refracted rays are mutually perpendicular. The angle of reflection and the angle of refraction are respectively r and r'. Then the critical angle will be: