A ray of monochromatic light is passing through an equilateral prism (ABC) as shown in the figure. The refracted ray (QR) is parallel to its base (BC) and the angle of incidence (i) is 50°. Then the angle of deviation ($\delta$) is: ____.
Show Hint
The phrase "parallel to the base" is a major hint. It mathematically implies symmetry ($i=e$ and $r_1=r_2$), which greatly simplifies prism problems.
Step 1: Understanding the Topic:
This problem belongs to "Ray Optics," specifically the refraction of light through a prism. It focuses on the special case of "Minimum Deviation," which occurs when the light path through the prism is perfectly symmetrical. Step 2: Key Formulas and Approach:
For any prism, the relationship between the angles is:
$\delta = i + e - A$ (where $\delta$ is deviation, $i$ is incidence, $e$ is emergence, and $A$ is prism angle).
If the ray inside the prism is parallel to the base of an isosceles/equilateral prism, then $i = e$.
Step 3: Detailed Explanation:
Determine Prism Angle (A): The problem states the prism is equilateral. In an equilateral triangle, all angles are $60^\circ$, so $A = 60^\circ$.
Identify the Symmetry Condition: The problem mentions the refracted ray (QR) is parallel to the base (BC). This is a physical condition that implies the angle of incidence ($i$) is equal to the angle of emergence ($e$).
Use given values: Given $i = 50^\circ$, it follows that $e = 50^\circ$.
Calculate Deviation: Plug the values into the prism formula:
\[ \delta = 50^\circ + 50^\circ - 60^\circ \]
\[ \delta = 100^\circ - 60^\circ = 40^\circ \]
This $40^\circ$ represents the total change in direction the light ray undergoes after passing through both faces of the prism.
Step 4: Final Answer:
The angle of deviation is 40°.
