in (figure 1) shown a rectangular glass block that has a metal reflector on one face and water on an adjoining face. a light beam strikes the reflector as shown. you gradually increase the angle $ \theta $ of the light beam. if $ \theta \geq 51.2^{\circ} $, no light enters the water. what is the speed of light in this glass?

part b
the target variable is the speed of light $ v $ in the glass, which you can determine from the index of refraction $ n $ of the glass. which equations will you use to find $ n $ and $ v $? check all that apply.
view available hint(s)
$ \sin \theta_a = n_b \sin \theta_b $
$ \sin \theta_{\text{crit}} = \frac{n_b}{n_a} $
$ v = \frac{c}{n} $
$ \lambda = \frac{\lambda_0}{n} $
$ \theta_r = \theta_a $
$ \tan \theta_p = \frac{n_b}{n_a} $
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Question

in (figure 1) shown a rectangular glass block that has a metal reflector on one face and water on an adjoining face. a light beam strikes the reflector as shown. you gradually increase the angle $ \theta $ of the light beam. if $ \theta \geq 51.2^{\circ} $, no light enters the water. what is the speed of light in this glass?

part b
the target variable is the speed of light $ v $ in the glass, which you can determine from the index of refraction $ n $ of the glass. which equations will you use to find $ n $ and $ v $? check all that apply.
view available hint(s)
$ \sin \theta_a = n_b \sin \theta_b $
$ \sin \theta_{\text{crit}} = \frac{n_b}{n_a} $
$ v = \frac{c}{n} $
$ \lambda = \frac{\lambda_0}{n} $
$ \theta_r = \theta_a $
$ \tan \theta_p = \frac{n_b}{n_a} $
submit
previous answers
incorrect; try again; one attempt remaining

Accepted Answer

# Brief Explanations:
To find $ n $ (refractive index of glass) and $ v $ (speed of light in glass), we analyze each equation:

1. **$\boldsymbol{\sin\theta_a = n_b \sin\theta_b}$**: This is Snell’s Law, relating angles of incidence ($\theta_a$) and refraction ($\theta_b$) to refractive indices ($n_a, n_b$) of two media. Applicable for refraction at the glass - water interface (or other interfaces here).
2. **$\boldsymbol{\sin\theta_{\text{crit}} = \frac{n_b}{n_a}}$**: This is the critical angle formula for total internal reflection, which may apply if total internal reflection occurs at the glass - water boundary (relevant to the problem’s context of light entering water).
3. **$\boldsymbol{v=\frac{c}{n}}$**: Relates the speed of light in a medium ($v$) to the speed of light in vacuum ($c$) and the refractive index ($n$) of the medium. Directly gives $ v $ once $ n $ is known.

The other equations are not relevant:
- $\lambda=\frac{\lambda_0}{n}$: Relates wavelength in medium to vacuum wavelength, not needed for $ n $ or $ v $ here.
- $\theta_r=\theta_a$: Describes reflection (angle of reflection = angle of incidence), not refraction or speed.
- $\tan\theta_p=\frac{n_b}{n_a}$: Relates to Brewster’s angle (polarization), not needed for $ n $ or $ v $ in this context.

# Answer:
$\sin\theta_a = n_b \sin\theta_b$, $\sin\theta_{\text{crit}} = \frac{n_b}{n_a}$, $v=\frac{c}{n}$

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