---
title: "A ray of white light in air is incident normally (\\(\\theta_1 = 0^\\circ\\)) on the first surface of a glass prism with apex angle \\(\\Phi\\), where \\(\\Phi\\) is less than the critical angle for the glass-air interface. The glass has an index of refraction \\(n\\) that depends on wavelength. The ray travels through the glass and refracts as it emerges from the second surface into air, deviating from its original path by a total angle \\(\\delta\\).  | Choice | Total Angle of Deviation \\(\\delta\\) | Wavelength with Greater Deviation | | :—: | :—: | :—: | | A | \\(\\arcsin(n \\sin\\Phi) + \\Phi\\) | Violet light | | B | \\(\\arcsin(n \\sin\\Phi) – \\Phi\\) | Violet light | | C | \\(\\arcsin\\left(\\dfrac{\\sin\\Phi}{n}\\right) – \\Phi\\) | Red light | | D | \\(\\arcsin(n \\sin\\Phi) – \\Phi\\) | Red light |  Which entry in the table correctly gives the expression for the total angle of deviation \\(\\delta\\) and identifies which visible component of the light experiences the greater deviation?"
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url: "https://nerd-notes.com/ubq/117452/"
date_modified: "2026-08-04T06:52:12+00:00"
---

# A ray of white light in air is incident normally (\(\theta_1 = 0^\circ\)) on the first surface of a glass prism with apex angle \(\Phi\), where \(\Phi\) is less than the critical angle for the glass-air interface. The glass has an index of refraction \(n\) that depends on wavelength. The ray travels through the glass and refracts as it emerges from the second surface into air, deviating from its original path by a total angle \(\delta\).

| Choice | Total Angle of Deviation \(\delta\) | Wavelength with Greater Deviation |
| :—: | :—: | :—: |
| A | \(\arcsin(n \sin\Phi) + \Phi\) | Violet light |
| B | \(\arcsin(n \sin\Phi) – \Phi\) | Violet light |
| C | \(\arcsin\left(\dfrac{\sin\Phi}{n}\right) – \Phi\) | Red light |
| D | \(\arcsin(n \sin\Phi) – \Phi\) | Red light |

Which entry in the table correctly gives the expression for the total angle of deviation \(\delta\) and identifies which visible component of the light experiences the greater deviation?

A ray of white light in air is incident normally (\(\theta_1 = 0^\circ\)) on the first surface of a glass prism with apex angle \(\Phi\), where \(\Phi\) is less than the critical angle for the glass-air interface. The glass has an index of refraction \(n\) that depends on wavelength. The ray travels through the glass and refracts as it emerges from the second surface into air, deviating from its original path by a total angle \(\delta\).

| Choice | Total Angle of Deviation \(\delta\) | Wavelength with Greater Deviation |
| :---: | :---: | :---: |
| A | \(\arcsin(n \sin\Phi) + \Phi\) | Violet light |
| B | \(\arcsin(n \sin\Phi) - \Phi\) | Violet light |
| C | \(\arcsin\left(\dfrac{\sin\Phi}{n}\right) - \Phi\) | Red light |
| D | \(\arcsin(n \sin\Phi) - \Phi\) | Red light |

Which entry in the table correctly gives the expression for the total angle of deviation \(\delta\) and identifies which visible component of the light experiences the greater deviation?

![A two-dimensional cross section of a triangular prism in air. The prism is drawn as an isosceles triangle pointing upward, with two equal slanted sides meeting at top vertex labeled with the Greek letter \Phi. The left slanted side represents the first refracting surface, and the right slanted side represents the second surface. A single horizontal ray line with a rightward arrowhead approaches from the left, perpendicular to the left slanted side. The ray passes straight into the prism without bending, continuing horizontally until it meets the right slanted side. At the intersection on the right slanted side, a dashed line segment is drawn perpendicular to the right surface to represent the surface normal. No emerging rays, refracted beams, angle labels other than \Phi, or color separations are drawn. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826332-wg7iYO.jpg)

- **A.** A
- **B.** B
- **C.** C
- **D.** D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117452/*