Step 2: Very Short Questions
a. Kerosene is considered an optically denser medium than water because its refractive index of 1.44 is higher than water’s 1.33, which causes light to travel more slowly through it.
b. The refractive index of glass remains constant even if the angle of incidence is increased because it represents a fixed ratio of the sine of the angle of incidence to the sine of the angle of refraction for a specific pair of media.
c. Medium A is the optically denser medium because the light ray is shown bending toward the normal as it enters from the first medium.
d. Light rays bend away from the normal when they pass from an optically denser medium, such as glass, into an optically rarer medium, such as air.
e. The rarer medium is the optical medium that has a relatively lower density and allows light to travel at a higher speed compared to a denser medium.
f. The critical angle for a medium with a refractive index of 1.65 is approximately 37.31 degrees.
g. The angle of incidence is equal to the critical angle of the denser medium when light passes into a rarer medium and the resulting angle of refraction is exactly 90°.
h. A mirage is an optical illusion seen on hot days where light rays from the sky are refracted through layers of air with different densities and then undergo total internal reflection near the ground.
i. The speed of light is maximum in water among the three listed media because water has the lowest refractive index of 1.33.
Step 3: Short Questions
a. The technology described in the story is known as endoscopy. It works on the principle of total internal reflection, where light is reflected inside optical fibers to illuminate and transmit images from within the body. The procedure is carried out by inserting a thin, flexible tube called an endoscope through natural body openings or small incisions, allowing doctors to view internal organs on a video monitor.
b. Differences between Keyhole Surgery and Endoscopy
Keyhole Surgery
- It is a surgical technique used for operations like removing stones or repairing internal organs.
- It is an invasive procedure that requires making small incisions in the patient’s skin.
- It involves the use of a specialized instrument called a laparoscope along with surgical tools.
- It results in smaller scars and a much faster recovery time compared to traditional open surgery.
Endoscopy - It is a diagnostic procedure used primarily for the visual examination of internal body cavities.
- It is generally non-invasive as it typically utilizes natural body openings like the mouth or rectum.
- It involves the use of a thin, flexible tube equipped with a light and a camera called an endoscope.
- It allows for the evaluation of organ conditions and the collection of tissue samples without surgery.
c. A ray diagram of a glass slab shows an incident ray entering from air, bending toward the normal inside the glass, and then bending away from the normal to emerge parallel to its original path.
d. To complete the diagrams: in the first, the ray bends toward the normal; in the second, the ray bends away from the normal; in the third, the ray bends toward the normal.
e. Refraction of light is the phenomenon where a light ray bends as it passes from one transparent medium to another with a different optical density. When an incident ray enters a glass slab from air, it moves from a rarer medium to a denser medium, which causes the speed of the light to decrease significantly. This change in velocity forces the light path to bend toward the normal to maintain the constant ratio defined by the refractive index. In conclusion, the light ray bends toward the normal because it travels more slowly in the denser medium of the glass slab.
f. The angle of incidence is the angle formed between the incident ray and the normal at the point where light hits a surface. When a light ray is perpendicular to the first face of a right-angled isosceles prism, it enters without deviation and strikes the second face at an angle of 45°. Since 45° exceeds the critical angle for glass, which is approximately 42°, the light ray cannot refract out and instead undergoes total internal reflection. In conclusion, the light will reflect back into the prism because the internal angle of incidence is greater than the critical angle.
g. To draw this diagram, illustrate a light ray in air meeting the water surface at an angle of 25° from the normal and then bending to an angle of 18.5° from the normal inside the water.
h. Fish A can see fish B without moving vertically by utilizing the total internal reflection of light at the water-air interface. The light rays traveling from fish B strike the surface of the water at an angle greater than the critical angle, causing the water’s surface to act like a mirror. These reflected rays then travel down toward fish A, allowing it to see a virtual image of fish B appearing on the surface of the water.
Step 4: Long Questions
a. Regarding the fiber net and tube:
∙ The thin flexible, hollow, and transparent tube is called an optical fiber.
∙ Its function is to transmit light signals and data over very long distances with high efficiency.
∙ It works on the principle of total internal reflection.
∙ Light entering the fiber strikes the inner boundary at an angle greater than the critical angle and reflects repeatedly until it emerges at the other end.
∙ It is preferred over copper wire because it can carry more information, is lighter, and is immune to electromagnetic interference.
b. Regarding Kunsang’s water bottle:
∙ The spectrum is known as the visible light spectrum or solar spectrum.
∙ There are seven colours in that spectrum: violet, indigo, blue, green, yellow, orange, and red.
∙ The spectrum is formed by the dispersion of light, where the water bottle acts as a prism to split white sunlight into its constituent colours because each colour travels at a different speed.
∙ A spectrum will not be formed everywhere because it requires specific angles of incidence for the light to refract and disperse effectively through the medium.
c. Regarding the dispersion diagram:
∙ (i) BA is the red colour and BG is the violet colour.
∙ (ii) Ray BG (violet) deviates the most because it has the shortest wavelength and travels at the slowest speed in glass, leading to maximum refraction.
∙ (iii) The colours found between BA and BG are orange, yellow, green, blue, and indigo.
d. Regarding the coin in the test tube:
∙ (i) The observer cannot see the coin because light from the coin undergoes total internal reflection at the air-water boundary inside the tube, preventing the light from reaching the eye.
∙ (ii) If water is filled in the test tube, the coin becomes visible because the air is removed, eliminating the interface that caused total internal reflection and allowing light to refract out to the observer.
Step 5: Numerical Problems
Problem 1: Refractive Index of Medium M
Solution:
Given Data:
∙ Speed of light in medium M, v = 0.75 × 10⁸ m/s
∙ Speed of light in vacuum, c = 3 × 10⁸ m/s
Formula:
μ = c/v
Calculation:
μ = (3 × 10⁸)/(0.75 × 10⁸)
μ = 3/0.75
μ = 4
Answer: The refractive index of medium M is 4.
Problem 2: Speed of Light in Diamond
Solution:
Given Data:
∙ Refractive index of diamond, μ = 2.42
∙ Speed of light in vacuum, c = 3 × 10⁸ m/s
Formula:
v = c/μ
Calculation:
v = (3 × 10⁸)/2.42
v = 1.239 × 10⁸ m/s
v = 1.24 × 10⁸ m/s
Answer: The speed of light in diamond is 1.24 × 10⁸ m/s.
Problem 3: Speed of Light in Water
Solution:
Given Data:
∙ Speed of light in vacuum, c = 3 × 10⁸ m/s
∙ Refractive index of water, μ = 1.33
Formula:
v = c/μ
Calculation:
v = (3 × 10⁸)/1.33
v = 2.255 × 10⁸ m/s
v = 2.25 × 10⁸ m/s
Answer: The speed of light in water is 2.25 × 10⁸ m/s.
Problem 4: Refractive Index of Glass
Solution:
Given Data:
∙ Angle of incidence, i = 15°
∙ Angle of refraction, r = 10°
Formula:
μ = sin i/sin r
Calculation:
μ = sin 15°/sin 10°
μ = 0.2588/0.1736
μ = 1.49
Answer: The refractive index of glass is 1.49.