LEVELJEE Main
Visualized Solution
The Sigma Insight: Refraction and Total Internal Reflection
Analyzing the Setup
Imagine a beam of light, composed of red, green, and blue colors, traveling towards a right-angled prism.
The beam strikes the vertical face of the prism normally. Because the angle of incidence is , the light passes straight through without any deviation.
It continues its journey inside the glass until it hits the slanted face, the hypotenuse of the prism.
The Geometry of Incidence
To understand what happens next, we need to look at the geometry of the prism.
It is a right-angled isosceles triangle, meaning the angle at the base is .
Using simple geometry, we can determine that the angle of incidence at the slanted face is exactly .
The Master Equation
Total Internal Reflection
Here is where the physics gets exciting. When light travels from a denser medium (glass) to a rarer medium (air), it can undergo Total Internal Reflection (TIR) if the angle of incidence is large enough.
The condition for TIR is that the angle of incidence must be strictly greater than the critical angle :
Taking the sine of both sides, we get:
We know that the sine of the critical angle is related to the refractive index by the equation .
Substituting our angle of , we find the critical condition for the refractive index:
This means that for any color of light to be totally internally reflected, its refractive index in the prism must be greater than 1.414.
Evaluating the Colors
Now, let's check the given refractive indices for our three colors.
For red light, . Since , red light does not meet the condition for TIR. It will be refracted and escape the prism.
For green light, . Since , green light undergoes TIR and is reflected entirely inside the prism.
For blue light, . Since , blue light also undergoes TIR and is reflected.
Final Conclusion
As a result of this beautiful interplay between geometry and optics, the red light escapes the prism through refraction, while the green and blue lights are trapped and reflected downwards.
Thus, the prism effectively separates the red color from the green and blue colors.
Similar Questions
JEE Main 2021
LEVELJEE Main
Three rays of light, namely red (R), green (G) and blue (B) are incident on the face PQ of a right angled prism PQR as shown in figure The refractive indices of the material of the prism for red, green and blue wavelength are 1.27, 1.42 and 1.49, respectively. The colour of the ray(s) emerging out of the face PR is
(A)
green
(B)
red
(C)
blue and green
(D)
blue
JEE Advanced 2010
LEVELJEE Advanced
A ray of monochromatic light is incident on the face of prism near vertex at an incident angle of (see figure). If the refractive index of the material of the prism is , which of the following is (are) correct?
* Multiple Correct Options
(A)
The ray gets totally internally reflected at face
(B)
The ray comes out through face
(C)
The angle between the incident ray and the emergent ray is
(D)
The angle between the incident ray and the emergent ray is
JEE Advanced 2013
LEVELJEE Advanced
A right angled prism of refractive index is placed in a rectangular block of refractive index , which is surrounded by a medium of refractive index , as shown in the figure. A ray of light 'e' enters the rectangular block at normal incidence. Depending upon the relationships between and , it takes one of the four possible paths 'ef', 'eg', 'eh' or 'ei'. Match the paths in Column I with conditions of refractive indices in Column II and select the correct answer using the codes given below the lists. \begin{array}{ll} \textbf{Column I} & \textbf{Column II} \\ \text{P. } e \rightarrow f & \text{1. } \mu_1 > \sqrt{2}\mu_2 \\ \text{Q. } e \rightarrow g & \text{2. } \mu_2 > \mu_1 \text{ and } \mu_2 > \mu_3 \\ \text{R. } e \rightarrow h & \text{3. } \mu_1 = \mu_2 \\ \text{S. } e \rightarrow i & \text{4. } \mu_2 < \mu_1 < \sqrt{2}\mu_2 \text{ and } \mu_2 > \mu_3 \end{array}
(A)
P-2, Q-3, R-1, S-4
(B)
P-1, Q-2, R-4, S-3
(C)
P-4, Q-1, R-2, S-3
(D)
P-2, Q-3, R-4, S-1
LEVELJEE Main
A light ray is incident perpendicular to one face of a prism and is totally internally reflected at the glass-air interface. If the angle of reflection is , we conclude that for the refractive index as
(A)
(B)
(C)
(D)
LEVELJEE Main
A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beam incident normally on the face is totally reflected to reach the face if
(A)
(B)
(C)
(D)
None of these
JEE Advanced 2001
LEVELJEE Main
A ray of light passes through four transparent media with refractive indices , , and as shown in the figure. The surfaces of all media are parallel. If the emergent ray is parallel to the incident ray , we must have
(A)
(B)
(C)
(D)
JEE Advanced 2016
LEVELJEE Advanced
A parallel beam of light is incident from air at an angle on the side of a right angled triangular prism of refractive index . Light undergoes total internal reflection in the prism at the face when has a minimum value of . The angle of the prism is
(A)
(B)
(C)
(D)
JEE Main 2004
LEVELJEE Main
White light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected then the emerging ray in air contains.
(A)
yellow, orange, red
(B)
violet, indigo, blue
(C)
all colours
(D)
all colours except green
JEE Advanced 1987
LEVELJEE Advanced
A right angled prism is to be made by selecting a proper material and the angles and (), as shown in figure. It is desired that a ray of light incident on the face emerges parallel to the incident direction after two internal reflections. (a) What should be the minimum refractive index for this to be possible? (b) For is it possible to achieve this with the angle equal to ?
JEE Advanced 2019
LEVELJEE Advanced