$14$A prism is an optical medium bounded by three refracting plane surfaces. A ray of light suffers successive refractions on passing through its two surfaces and deviates by a certain angle from its original path. The refractive index of the material of the prism is given by $\displaystyle \mu=\sin \left(\frac{\mathrm{A}+\delta \mathrm{m}}{2}\right) / \sin \frac{\mathrm{A}}{2}$. If the angle of incidence on the second surface is greater than an angle called critical angle, the ray will not be refracted from the second surface and is totally internally reflected. (i) The critical angle for glass is $\displaystyle \theta_{1}$ and that for water is $\displaystyle \theta_{2}$. The critical angle for glass-water surface would be (given $\displaystyle { }_{\mathrm{a}} \mu_{\mathrm{g}}=1.5$, $\displaystyle { }_{\mathrm{a}} \mu_{\mathrm{w}}=1.33$ ) (A) less than $\displaystyle \theta_{2}$ (B) between $\displaystyle \theta_{1}$ and $\displaystyle \theta_{2}$ (C) greater than $\displaystyle \theta_{2}$ (D) less than $\displaystyle \theta_{1}$ (ii) When a ray of light of wavelength $\displaystyle \lambda$ and frequency $\displaystyle v$ is refracted into a denser medium (A) $\displaystyle \lambda$ and $\displaystyle v$ both increase. (B) $\displaystyle \lambda$ increases but $\displaystyle v$ is unchanged. (C) $\displaystyle \lambda$ decreases but $\displaystyle v$ is unchanged. (D) $\displaystyle \lambda$ and $\displaystyle v$ both decrease. (iii) (a) The critical angle for a ray of light passing from glass to water is minimum for (A) red colour (B) blue colour (C) yellow colour (D) violet colour

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(iii) (b) Three beams of red, yellow and violet colours are passed through a prism, one by one under the same condition. When the prism is in the position of minimum deviation, the angles of refraction from the second surface are $\displaystyle \mathrm{r}_{\mathrm{R}}, \mathrm{r}_{\mathrm{Y}}$ and $\displaystyle \mathrm{r}_{\mathrm{V}}$ respectively. Then (A) $\displaystyle \mathrm{r}_{\mathrm{V}}<\mathrm{r}_{\mathrm{Y}}<\mathrm{r}_{\mathrm{R}}$ (B) $\displaystyle \mathrm{r}_{\mathrm{Y}}<\mathrm{r}_{\mathrm{R}}<\mathrm{r}_{\mathrm{V}}$ (C) $\displaystyle \mathrm{r}_{\mathrm{R}}<\mathrm{r}_{\mathrm{Y}}<\mathrm{r}_{\mathrm{V}}$ (D) $\displaystyle \mathrm{r}_{\mathrm{R}}=\mathrm{r}_{\mathrm{Y}}=\mathrm{r}_{\mathrm{V}}$ (iv) A ray of light is incident normally on a prism ABC of refractive index $\displaystyle \sqrt{2}$, as shown in figure. After it strikes face AC, it will 2024_CBSE_Physics_Set_Region5_Subset_Set1_Q30__iv_p9_27

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(A) go straight undeviated (B) just graze along the face AC (C) refract and go out of the prism (D) undergo total internal reflection

Physics · Ray Optics and Optical Instruments · Refraction through a Prism