When a narrow beam of white light passes through a glass prism, it splits into a spectrum of seven colors. Whi

Question

When a narrow beam of white light passes through a glass prism, it splits into a spectrum of seven colors. Which of the following statements is true regarding this phenomenon?

Examoogle · Accepted Answer

The correct answer is Option C: Red light bends the least because it has the longest wavelength. When white light enters a glass prism, it undergoes dispersion due to the different speeds of its constituent colors in the glass medium. Red light has the longest wavelength and travels fastest in glass, causing it to bend the least, while violet light has the shortest wavelength and bends the most.

Step-by-Step Solution & Concepts:
When white light enters a glass prism, it undergoes dispersion due to the different speeds of its constituent colors in the glass medium. Red light has the longest wavelength and travels fastest in glass, causing it to bend the least, while violet light has the shortest wavelength and bends the most.

Working Principle: The refractive index of a material is dependent on the wavelength of light, a phenomenon known as chromatic dispersion. According to Cauchy's equation, $n(\lambda) = A + \frac{B}{\lambda^2} + \dots$, shorter wavelengths experience a higher refractive index $n$ and thus deviate more from their original path based on Snell's Law, $n_1 \sin(i) = n_2 \sin(r)$.

Key Formulas: $\delta = (n - 1)A$ — approximate formula for deviation $\delta$ in a thin prism of angle $A$; $\lambda = \frac{v}{f}$ — relation between wavelength, velocity, and frequency

Key Points: Dispersion is the separation of white light into its spectrum.; The refractive index of glass is higher for violet light than for red light.; Frequency remains constant when light passes through a medium, but speed and wavelength change.

Advantages: Explains the formation of rainbows in nature.

Disadvantages: Chromatic aberration in lenses which leads to blurred images.

Applications: Spectroscopy for chemical analysis; Design of optical prisms and lenses

Additional Info: Speed of light in glass: $v = \frac{c}{n}$, where $c \approx 3 	imes 10^8 	ext{ m/s}$.. Option A is false because speed varies with color; Option B is false because violet bends the most; Option D is false because dispersion is caused by refraction, not reflection.

Answer: C is correct — Red light bends the least because it has the longest wavelength, leading to the smallest change in refractive index and minimum angular deviation.

Exam Tip: Remember that for any light passing through a medium, frequency is determined by the source and remains constant, while speed and wavelength change relative to each other.

Examoogle · Answer

Option A: The speed of all colors is the same in the prism

Examoogle · Answer

Option B: Violet light bends the least because it has the shortest wavelength

Examoogle · Answer

Option D: The dispersion is caused by the reflection of light inside the prism

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)