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Questions and Answers
A ray of light enters a glass sphere with a refractive index of $\sqrt{3}$. The ray is incident at an angle $i$. At the farther surface, the angle between the reflected and refracted rays is 90°. Determine the value of the angle $i$.
A ray of light enters a glass sphere with a refractive index of $\sqrt{3}$. The ray is incident at an angle $i$. At the farther surface, the angle between the reflected and refracted rays is 90°. Determine the value of the angle $i$.
- $\frac{\pi}{6}$
- $\frac{\pi}{3}$ (correct)
- $\frac{2\pi}{3}$
- $\frac{\pi}{4}$
A cylindrical optical fiber with a refractive index of 2 and a diameter of 4mm is surrounded by air. A light beam is sent into the fiber along its axis. What is the smallest outer radius R for which no light escapes during first refraction from the curved surface?
A cylindrical optical fiber with a refractive index of 2 and a diameter of 4mm is surrounded by air. A light beam is sent into the fiber along its axis. What is the smallest outer radius R for which no light escapes during first refraction from the curved surface?
- 4mm
- 6 mm
- 2mm
- 8 mm (correct)
A ray of light is incident from air on a sphere with a refractive index of $\sqrt{2}$. If the angle of refraction inside the sphere is 30°, what is the total deviation suffered by the ray?
A ray of light is incident from air on a sphere with a refractive index of $\sqrt{2}$. If the angle of refraction inside the sphere is 30°, what is the total deviation suffered by the ray?
- 90°
- 120°
- 45°
- 150° (correct)
The xz-plane separates two media, A and B, with refractive indices $\mu_1$ and $\mu_2$, respectively. A ray of light travels from A to B. The directions in the two media are given by the unit vectors $r_A = a\hat{i} + b\hat{j}$ and $r_B = \alpha\hat{i} + \beta\hat{j}$, where $\hat{i}$ and $\hat{j}$ are unit vectors in the x and y directions. Which of the following relations is correct?
The xz-plane separates two media, A and B, with refractive indices $\mu_1$ and $\mu_2$, respectively. A ray of light travels from A to B. The directions in the two media are given by the unit vectors $r_A = a\hat{i} + b\hat{j}$ and $r_B = \alpha\hat{i} + \beta\hat{j}$, where $\hat{i}$ and $\hat{j}$ are unit vectors in the x and y directions. Which of the following relations is correct?
A beaker is filled with water. The bottom is a concave mirror. The water height is 40 cm. An object placed 4 cm above the water coincides with its image. If the water level is reduced to zero, what new height of the object above the surface will make the image coincide with the object? (Refractive index of water = 4/3)
A beaker is filled with water. The bottom is a concave mirror. The water height is 40 cm. An object placed 4 cm above the water coincides with its image. If the water level is reduced to zero, what new height of the object above the surface will make the image coincide with the object? (Refractive index of water = 4/3)
A light ray traveling in glass strikes a glass-air interface. Which plot correctly shows the reflected (R) and transmitted (T) intensities as a function of incidence angle $\theta$?
A light ray traveling in glass strikes a glass-air interface. Which plot correctly shows the reflected (R) and transmitted (T) intensities as a function of incidence angle $\theta$?
A parallel beam of light is incident from air on a right-angled triangular prism with refractive index $n = \sqrt{2}$ at an angle $\alpha$ on side PQ. If light undergoes total internal reflection at face PR with a minimum $\alpha$ of 45°, and $\theta$ is the angle if the prism, then the angle $\theta$ of the prism greater than 45 degrees. Is this statement true or false?
A parallel beam of light is incident from air on a right-angled triangular prism with refractive index $n = \sqrt{2}$ at an angle $\alpha$ on side PQ. If light undergoes total internal reflection at face PR with a minimum $\alpha$ of 45°, and $\theta$ is the angle if the prism, then the angle $\theta$ of the prism greater than 45 degrees. Is this statement true or false?
A ray of light strikes a plane mirror at an incidence angle of 45°. After reflection, it passes through a prism with a refractive index of 1.5 and an apex angle of 4°. To achieve a total deviation of 90°, by how many degrees should the mirror be rotated?
A ray of light strikes a plane mirror at an incidence angle of 45°. After reflection, it passes through a prism with a refractive index of 1.5 and an apex angle of 4°. To achieve a total deviation of 90°, by how many degrees should the mirror be rotated?
In a setup with a convex lens forming an inverted image on a fixed screen, the image size is initially 12 cm. After displacing the lens by 20 cm, the image size becomes 3 cm. Assuming paraxial rays, the focal length of the lens is ______ cm.
In a setup with a convex lens forming an inverted image on a fixed screen, the image size is initially 12 cm. After displacing the lens by 20 cm, the image size becomes 3 cm. Assuming paraxial rays, the focal length of the lens is ______ cm.
Match the optical elements with their corresponding optical power characteristics:
Match the optical elements with their corresponding optical power characteristics:
Flashcards
Critical Angle
Critical Angle
The angle of incidence at which light undergoes total internal reflection.
Refraction
Refraction
The bending of light as it passes from one medium to another.
Refractive index
Refractive index
A measure of how much a medium slows down the speed of light.
Brewster's Angle
Brewster's Angle
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Lenses
Lenses
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Concave Mirrors
Concave Mirrors
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Convex Mirrors
Convex Mirrors
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Light scattering
Light scattering
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Diffraction
Diffraction
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Study Notes
- These notes cover geometrical optics and related physics problems.
Problem 1
- A ray enters a glass sphere at an incidence angle
i, reflects, and refracts at the far surface. - The angle between reflected and refracted rays at this surface is 90°.
- Refractive index of the sphere is √3.
Problem 2
- A cylindrical optical fiber has a quarter-circular shape with refractive index n = 2 and diameter d = 4mm, surrounded by air.
- A light beam enters along its axis.
- Find the smallest outer radius R for which no light escapes during the first refraction from the curved surface.
Problem 3
- A ray is incident from air on a sphere with refractive index √2.
- The angle of refraction inside the sphere is 30°.
- Determine the total deviation suffered by the ray.
Problem 4
- The xz plane separates two media A and B with refractive indices μ₁ and μ₂.
- A light ray travels from A to B with unit direction vectors r₁ = ai + bj and r₂ = αi + βj.
Problem 5
- A beaker is filled with water, and its bottom surface is a concave mirror with a large radius of curvature.
- The water height is h = 40 cm.
- An object placed 4 cm above the water surface has its image coinciding with the object.
- The water level
his then reduced to zero. - Determine the new object height above the new water surface for the image to coincide with the object again, given the water's refractive index is 4/3.
Problem 6
- A glass slab has a refractive index n = 1 + ax, where a = 1 cm⁻¹, and
xis the perpendicular distance from face AB. - Determine the shift in the object's position.
Problem 7
- A light ray travels in a glass medium and is incident on a glass-air interface at an angle of incidence θ.
- Reflected (R) and transmitted (T) intensities are plotted as functions of θ.
Problem 8
- Parallel light beam incidents from air at angle α on side PQ of a right-angled triangular prism.
- Prism's refraction index n = √2
- Light undergoes total internal reflection at face PR when α has a minimum value of 45°.
- Determine angle θ of the prims
Problem 9
- A wire is bent into a right-angled triangle and placed in front of a concave mirror with focal length f.
- Identify which figure represents the shape of the image of the bent wire.
Problem 10
- A light ray strikes a plane mirror at 45°.
- After reflection, passes through a prism with refractive index 1.5 and apex angle 4°.
- Find the rotation angle so the total deviation is 90°.
Problem 11
- A convex lens forms an inverted image of a real object on a fixed screen; image size is 12 cm.
- Displacing the lens by 20 cm forms another real image of size 3 cm.
- Determine the lens's focal length, assuming paraxial rays.
Problem 12
- Face PR of a prism QPR with angle 30° is silvered.
- Ray incidents on face PQ with 45°.
- Refracted ray reflects on face PR and retraces its path.
- Find refractive index of the prism
Problem 13
- A point object is placed at a distance of (5R)/3 from a concave mirror with radius of curvature R.
- The object oscillates with 1mm amplitude perpendicular to the optical axis.
- Determine properties of the image.
Problem 14
- A graph plots deviation angle (δ) vs. incidence angle (i) for a prism.
- Identify angle of prism, and refractive index.
Problem 15
- A small air bubble is trapped in a 12 cm transparent cube.
- It appears at 5 cm from one face and 3 cm from the opposite face.
- Determine the air bubble's distance from the first face and the cube's refractive index.
Problem 16
- A diagram shows a real image point P' formed through a lens or optical system.
- Determine different actions will move point farthest from the boundary.
Problem 17
- A concave mirror has a radius of curvature of 20 cm.
- A circular disc of diameter 1 cm is placed 15 cm from the mirror pole, perpendicular to the principal axis.
- The disc's radius increases according to r = (0.5 + 0.1t) cm/sec.
- Determine the image shape.
Problem 18
- What is the area of the image of the disc when t=1.
Problem 19
- The rate at which the radius of image will be changing.
Problem 20
- Object lies in front of a thick parralel glass slab.
- Bottom of slab is polished.
- Distance between the first two images formes is 4cm.
- Find thickness of the slab, where the nglass = 3.2
Problem 21
- Find "t", of the max time taken by a ray to exit plan CD is t * 10^-9 seconds.
Problem 22
- Optical power for different lens configurations.
Problem 23
- A fly is sitting on a glass slab S 45cm thich of refraction index 3/2
- The slab covers the top of a container C containing water of hight 20cm.
- Bottom of container is closed by a concave mirror of radius of curvature of 40 cm
- Locate the final image
Problem 24
- a paper weight of refraction index of n = 3/2 with radius 3.0 cm is holding print
- An observer is looking at the page, what height above the paper will print to show the observer.
- Solve the problem if paperwight is inverted.
Problem 25
- A ray of light strikes a glass slab of thiccness t at an angle of incidence theta, prove that for a small angle incidents the lateral shift y is given by y= ttheta(1-1/n) n is the refraction index with respect to air
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