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 : 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 :
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 :
Important Questions from Optics
- The magnitudes of power of a biconvex lens (refractive index $1.5$) and that of a plano-concave lens (refractive index = $1.7$) are same. If the curvature of plano-concave lens exactly matches with the curvature of back surface of the biconvex lens, then ratio of radius of curvature of front and back surface of the biconvex lens is ________.
- Given below are two statements:
**Statement I:** A plane wave after passing through prism remains as plane wave but passing through small pin hole may become spherical wave.
**Statement II:** The curvature of a spherical wave emerging from a slit will increase for increasing slit width.
In the light of the above statements, choose the correct answer from the options given below - A convex lens of refractive index $1.5$ and focal length $f = 18 \text{ cm}$ is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is $\alpha \times f$. The value of $\alpha$ is ________.
(refractive index of water = $4/3$) - Consider an equilateral prism (refractive index $\sqrt{2}$). A ray of light is incident on its one surface at a certain angle $i$. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to _________.
- A thin convex lens of focal length 5 cm and a thin concave lens of focal length 4 cm are combined together (without any gap) and this combination has magnification $m_1$ when an object is placed 10 cm before the convex lens. Keeping the positions of convex lens and object undisturbed a gap of 1 cm is introduced between the lenses by moving the concave lens away, which lead to a change in magnification of total lens system to $m_2$. The value of $\left| \frac{m_1}{m_2} \right|$ is _________.
