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A glass prism has refractive index 1.5 and the refracting angle 90° If a ray falls on it at an angle
of incidence of 30°, then the angle of emergence will be
- a)60°
- b)45°
- c)30°
- d)the ray will not emerge at all
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A glass prism has refractive index 1.5 and the refracting angle 90°...
We have, ( 1.5-1) *90
= 0.5 *90 ⇒ 45°
Now, 45-30+90°
⇒ 105°
Angle of emergence has inclination with second surface.
⇒ 90 - 105
⇒ -15
This shows that light ray will not emerge out of the prism.
= 0.5 *90 ⇒ 45°
Now, 45-30+90°
⇒ 105°
Angle of emergence has inclination with second surface.
⇒ 90 - 105
⇒ -15
This shows that light ray will not emerge out of the prism.
Most Upvoted Answer
A glass prism has refractive index 1.5 and the refracting angle 90°...
We have, ( 1.5-1) *90
= 0.5 *90 ⇒ 45°
Now, 45-30+90°
⇒ 105°
Angle of emergence has inclination with second surface.
⇒ 90 - 105
⇒ -15
This shows that light ray will not emerge out of the prism.
= 0.5 *90 ⇒ 45°
Now, 45-30+90°
⇒ 105°
Angle of emergence has inclination with second surface.
⇒ 90 - 105
⇒ -15
This shows that light ray will not emerge out of the prism.
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Community Answer
A glass prism has refractive index 1.5 and the refracting angle 90°...
- **Explanation:**
- **Refractive Index and Refracting Angle:**
- The refractive index of the prism is given as 1.5, and the refracting angle is 90°.
- **Angle of Incidence and Angle of Emergence:**
- When a ray falls on the prism at an angle of incidence of 30°, it will be refracted according to the laws of refraction.
- The angle of emergence can be calculated using Snell's Law, which states:
- n1 * sin(angle of incidence) = n2 * sin(angle of emergence)
- Here, n1 is the refractive index of the medium before the prism (air, which is 1), n2 is the refractive index of the prism (1.5), the angle of incidence is 30°, and we need to find the angle of emergence.
- **Calculation:**
- Plugging in the values, we get:
- 1 * sin(30°) = 1.5 * sin(angle of emergence)
- sin(30°) = 1.5 * sin(angle of emergence)
- 0.5 = 1.5 * sin(angle of emergence)
- sin(angle of emergence) = 0.5 / 1.5
- sin(angle of emergence) = 1/3
- angle of emergence = sin^(-1)(1/3) = 19.47°
- **Conclusion:**
- The angle of emergence is calculated to be approximately 19.47°, which is less than the critical angle for total internal reflection (which would be 41.81° in this case).
- Hence, the ray will not emerge at all from the prism and will undergo total internal reflection.
- **Refractive Index and Refracting Angle:**
- The refractive index of the prism is given as 1.5, and the refracting angle is 90°.
- **Angle of Incidence and Angle of Emergence:**
- When a ray falls on the prism at an angle of incidence of 30°, it will be refracted according to the laws of refraction.
- The angle of emergence can be calculated using Snell's Law, which states:
- n1 * sin(angle of incidence) = n2 * sin(angle of emergence)
- Here, n1 is the refractive index of the medium before the prism (air, which is 1), n2 is the refractive index of the prism (1.5), the angle of incidence is 30°, and we need to find the angle of emergence.
- **Calculation:**
- Plugging in the values, we get:
- 1 * sin(30°) = 1.5 * sin(angle of emergence)
- sin(30°) = 1.5 * sin(angle of emergence)
- 0.5 = 1.5 * sin(angle of emergence)
- sin(angle of emergence) = 0.5 / 1.5
- sin(angle of emergence) = 1/3
- angle of emergence = sin^(-1)(1/3) = 19.47°
- **Conclusion:**
- The angle of emergence is calculated to be approximately 19.47°, which is less than the critical angle for total internal reflection (which would be 41.81° in this case).
- Hence, the ray will not emerge at all from the prism and will undergo total internal reflection.
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A glass prism has refractive index 1.5 and the refracting angle 90° If a ray falls on it at an angleof incidence of 30°, then the angle of emergence will bea)60°b)45°c)30°d)the ray will not emerge at allCorrect answer is option 'D'. Can you explain this answer?
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