A ray of monochromatic light is passing through an equilateral prism (ABC) as shown in the figure. The refracted ray (QR) is parallel to the base (BC) and the angle of incidence ($i$) is $50^\circ$. Then the angle of deviation ($\delta$) is :
To solve this problem, it is essential to understand the refraction of light through a prism and how the angle of deviation is determined in such scenarios.
Given Data:
- The prism is equilateral, meaning all its angles are \(60^\circ\).
- The angle of incidence \(i = 50^\circ\).
- The refracted ray \(QR\) is parallel to the base \(BC\).
Concept and Calculation:
- In an equilateral prism, the refracted ray \(QR\) being parallel to the base indicates that the angle of refraction at \(Q\) and exit angle at \(R\) combined will equal the angle of the prism. Therefore, the angle of refraction \(r\) at both \(Q\) and \(R\) is \(30^\circ\).
- This situation is depicted by using Snell’s Law at the first surface: \(n \sin i = \sin r\), where \(i = 50^\circ\) and \(r = 30^\circ\).
- The angle of deviation \(\delta\) is given by the formula: \(\delta = i + e - A\), where \(e\) is the angle of emergence and \(A\) is the angle of the prism.
- Since \(r_1 = r_2\) and the angle of the prism \(A = 60^\circ\), the angle of emergence \(e\) is also \(50^\circ\).
- Substituting the values, we have: \(\delta = 50^\circ + 50^\circ - 60^\circ = 40^\circ\).
Therefore, the angle of deviation \(\delta\) is 40°.
Conclusion: The correct answer is 40°, as it matches the angle of deviation calculated.
Similar Questions
- In Young's double slit experiment, using monochromatic light of wavelength $\lambda$, the intensity of light at a point on the screen where the path difference is $\lambda$, is $K$ units. The intensity of light at a point where the path difference is $\lambda/3$ will be :
- In a concave lens, a ray of light emanating from the object parallel to the principal axis of the lens, after refraction :
- In interference and diffraction, the light energy is redistributed. If it reduces in one region, producing a dark fringe, it increases in another region, producing a bright fringe.
A. As there is no gain or loss of energy, these phenomena are consistent with the principle of conservation of energy.
B. Diffraction and interference are characteristics exhibited only by light waves.
Choose the correct answer from the options given below : Consider three media P, Q and R with refractive indices $1$, $1.25$, and $1.5$, respectively. The medium Q having a thickness of $5\text{ cm}$ is placed between extended media P and R as shown in the figure. An object O is placed at the center of medium Q. If viewed from medium P near the normal direction, the apparent depth of O is $h_1$. For similar observation from medium R, the apparent depth is $h_2$. The value of $|h_1 - h_2|$, in cm, is :
The lens combination as shown in the figure, consists of two lenses, $L_1$ and $L_2$, of the focal lengths $+10\text{ cm}$ and $-10\text{ cm}$, respectively. The position of the image formed is :
Important Questions from Optics
- In a microscope the objective is having focal length $f_o = 2 \text{ cm}$ and eye-piece is having focal length $f_e = 4 \text{ cm}$. The tube length is $32 \text{ cm}$. The magnification produced by this microscope for normal adjustment is ____________.
- A collimated beam of light of diameter $2 \text{ mm}$ is propagating along x-axis. The beam is required to be expanded in a collimated beam of diameter $14 \text{ mm}$ using a system of two convex lenses. If first lens has focal length $40 \text{ mm}$, then the focal length of second lens is ____________ $\text{mm}$.
- In a Young's double slit experiment set up, the two slits are kept $0.4\text{ mm}$ apart and screen is placed at $1\text{ m}$ from slits. If a thin transparent sheet of thickness $20 \, \mu\text{m}$ is introduced in front of one of the slits then center bright fringe shifts by $20\text{ mm}$ on the screen. The refractive index of transparent sheet is given by $\frac{\alpha}{10}$, where $\alpha$ is __________.
- In two separate Young's double-slit experimental set-ups and two monochromatic light sources of different wavelengths are used to get fringes of equal width. The ratios of the slits separations and that of the wavelengths of light used are $2 : 1$ and $1 : 2$ respectively. The corresponding ratio of the distances between the slits and the respective screens ($D_1/D_2$) is ___________.
- The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions $8 \text{ cm}$ and $24 \text{ cm}$ from the lens. The focal length of the lens is ________ $\text{cm}$.
