A thin prism $P_1$ of angle $4^\circ$ and refractive index 1.54 is combined with another thin prism $P_2$ of refractive index 1.72 to produce dispersion without deviation. The angle of $P

Explore Exams

All Exams Test series for 1 year @ ₹349 only

Question

RRB ALP - 2018

A thin prism $P_1$ of angle $4^\circ$ and refractive index 1.54 is combined with another thin prism $P_2$ of refractive index 1.72 to produce dispersion without deviation. The angle of $P_2$ is

This question was previously asked in

RRB ALP 2018 CBT 2 Fitter Question Paper (21-Jan-2019) (Shift 3)

Attempt Now

$3^\circ$

$2.6^\circ$

$4^\circ$

$5.33^\circ$

The correct answer is

$3^\circ$

To solve the given problem, we need to understand the concept of how two prisms are combined to produce dispersion without deviation. This occurs when the angle of deviation due to one prism cancels out the angle of deviation due to the other prism.

The conditions for the elimination of deviation while maintaining dispersion is defined by the relationship:

$(\mu_1 - 1)A_1 = (\mu_2 - 1)A_2$

where:

$\mu_1$ = Refractive index of prism $P_1$
$A_1$ = Angle of prism $P_1$
$\mu_2$ = Refractive index of prism $P_2$
$A_2$ = Angle of prism $P_2$

Given:

$\mu_1 = 1.54$
$A_1 = 4^\circ$
$\mu_2 = 1.72$
We need to find $A_2$.

Substitute the given values into the equation:

$(1.54 - 1) \times 4 = (1.72 - 1) \times A_2$

This simplifies to:

$0.54 \times 4 = 0.72 \times A_2$

Calculate the left-hand side:

$2.16 = 0.72 \times A_2$

Now, solve for $A_2$:

$A_2 = \frac{2.16}{0.72} = 3^\circ$

Therefore, the angle of prism $P_2$ must be $3^\circ$ to achieve dispersion without deviation. Hence, the correct option is 3°.

Was this answer helpful?

Important Questions from Optics

Which among the following is used as a reflector in search lights?
General Science
View Answer
The incident ray, the ray perpendicular to the point of incidence, and the reflected ray all lie________.
General Science
View Answer
Which is the only event to prove that light is a transverse wave?
A. Scattering of light
B. Interference
C. Diffraction
D. Polarisation
General Science
View Answer
In which a convex mirror is used?
A. Rear View mirrors in vehicles
B. Glass windows
C. Makeup Mirror
D. Kaleidoscope
Physics
View Answer
Which mirror is preferred as a rear-view (wing) mirror in vehicles because of its wider field of view?
General Science
View Answer