Question:
Consider the statements given below and choose the correct option :
Statement 1 : Angle of deviation produced by a prism depends on the angle of the prism.
Statement 2 : Dispersion takes place in a prism because the refractive index of the refracting medium is different for different wavelengths.
Consider the statements given below and choose the correct option :
Statement 1 : Angle of deviation produced by a prism depends on the angle of the prism.
Statement 2 : Dispersion takes place in a prism because the refractive index of the refracting medium is different for different wavelengths.
Statement 1 : Angle of deviation produced by a prism depends on the angle of the prism.
Statement 2 : Dispersion takes place in a prism because the refractive index of the refracting medium is different for different wavelengths.
Show Hint
Violet light has the shortest wavelength, highest refractive index, and undergoes the maximum deviation.
Red light has the longest wavelength, lowest refractive index, and undergoes the minimum deviation.
Red light has the longest wavelength, lowest refractive index, and undergoes the minimum deviation.
Updated On: Jul 13, 2026
- Statements 1 & 2 both are correct.
- Statement 1 is correct, but Statement 2 is incorrect.
- Statements 1 & 2 both are incorrect.
- Statement 1 is incorrect, but Statement 2 is correct.
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
The question presents two statements regarding light refraction, deviation, and dispersion through a glass prism and asks to evaluate the accuracy of both statements.
Step 2: Key Formula or Approach:
Recall the prism formula for the angle of deviation (\(\delta\)):
\[ \delta = i + e - A \] where \(A\) is the angle of the prism.
Also recall Cauchy's relation for refractive index (\(\mu\)) and wavelength (\(\lambda\)):
\[ \mu(\lambda) \approx a + \frac{b}{\lambda^2} \]
Step 3: Detailed Explanation:
• Statement 1: The angle of deviation (\(\delta\)) is the angle between the incident ray and the emergent ray. Mathematically, \(\delta = i + e - A\). This formula directly contains the angle of the prism (\(A\)). Thus, the deviation depends on the angle of the prism. Statement 1 is correct.
• Statement 2: White light is composed of multiple colors (wavelengths). According to Cauchy's relation, the refractive index of glass is different for different wavelengths (highest for violet, lowest for red). Since the bending of light depends on the refractive index, different wavelengths bend by different angles upon entering and leaving the prism, causing the white light to split into its component colors (dispersion). Thus, Statement 2 is correct.
Step 4: Final Answer:
Both statements 1 and 2 are correct.
The question presents two statements regarding light refraction, deviation, and dispersion through a glass prism and asks to evaluate the accuracy of both statements.
Step 2: Key Formula or Approach:
Recall the prism formula for the angle of deviation (\(\delta\)):
\[ \delta = i + e - A \] where \(A\) is the angle of the prism.
Also recall Cauchy's relation for refractive index (\(\mu\)) and wavelength (\(\lambda\)):
\[ \mu(\lambda) \approx a + \frac{b}{\lambda^2} \]
Step 3: Detailed Explanation:
• Statement 1: The angle of deviation (\(\delta\)) is the angle between the incident ray and the emergent ray. Mathematically, \(\delta = i + e - A\). This formula directly contains the angle of the prism (\(A\)). Thus, the deviation depends on the angle of the prism. Statement 1 is correct.
• Statement 2: White light is composed of multiple colors (wavelengths). According to Cauchy's relation, the refractive index of glass is different for different wavelengths (highest for violet, lowest for red). Since the bending of light depends on the refractive index, different wavelengths bend by different angles upon entering and leaving the prism, causing the white light to split into its component colors (dispersion). Thus, Statement 2 is correct.
Step 4: Final Answer:
Both statements 1 and 2 are correct.
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