---
title: "A transparent triangular prism with an apex angle \\(\\alpha\\) is submerged in a fluid of refractive index \\(n_{\\text{fluid}}\\). A ray of monochromatic light traveling in the fluid strikes the vertical leg of the prism at normal incidence and travels to the hypotenuse face, as shown. The speed of light in a vacuum is \\(c\\). Which of the following expressions represents the maximum speed of light inside the prism, \\(v_{\\text{prism}}\\), for which total internal reflection will still occur at the hypotenuse face?"
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url: "https://nerd-notes.com/ubq/116919/"
date_modified: "2026-08-04T06:10:06+00:00"
---

# A transparent triangular prism with an apex angle \(\alpha\) is submerged in a fluid of refractive index \(n_{\text{fluid}}\). A ray of monochromatic light traveling in the fluid strikes the vertical leg of the prism at normal incidence and travels to the hypotenuse face, as shown. The speed of light in a vacuum is \(c\). Which of the following expressions represents the maximum speed of light inside the prism, \(v_{\text{prism}}\), for which total internal reflection will still occur at the hypotenuse face?

A transparent triangular prism with an apex angle \(\alpha\) is submerged in a fluid of refractive index \(n_{\text{fluid}}\). A ray of monochromatic light traveling in the fluid strikes the vertical leg of the prism at normal incidence and travels to the hypotenuse face, as shown. The speed of light in a vacuum is \(c\). Which of the following expressions represents the maximum speed of light inside the prism, \(v_{\text{prism}}\), for which total internal reflection will still occur at the hypotenuse face?

![A right-angled triangular cross-section of a prism in a two-dimensional plane. The left face is vertical and the bottom face is horizontal, meeting at a 90-degree right angle at the bottom-left vertex. The top vertex has an interior apex angle labeled \(\alpha\). A horizontal incident light ray with an arrowhead pointing to the right enters the vertical left face perpendicularly at normal incidence. Inside the prism, the ray continues horizontally as a dashed line until it meets the slanted hypotenuse face. At the point of contact on the hypotenuse face, a dashed normal line is drawn perpendicular to the hypotenuse, extending outside and inside the prism. The angle between the horizontal ray inside the prism and the dashed normal line is labeled \(\alpha\). The region outside the prism is labeled \(n_{\text{fluid}}\), and the region inside the prism is labeled \(v_{\text{prism}}\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785823806-CgWAp8.jpg)

- **A.** \(v_{\text{prism}} = \dfrac{c}{n_{\text{fluid}} \sin\alpha}\)
- **B.** \(v_{\text{prism}} = \dfrac{c \text{ } n_{\text{fluid}}}{\sin\alpha}\)
- **C.** \(v_{\text{prism}} = \dfrac{c \cos\alpha}{n_{\text{fluid}}}\)
- **D.** \(v_{\text{prism}} = \dfrac{c \sin\alpha}{n_{\text{fluid}}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116919/*