Class 10 Physics: Refraction and Refractive Index with Solved Numericals

A pencil appears bent at the surface of water because light changes direction as it passes between water and air. Refraction questions test whether you can connect that observation with the normal, the angle of incidence and the speed of light in a medium. This lesson explains those connections before using numbers. The aim is to make each calculation follow from a sketch rather than a remembered sentence.

Use this as topic practice alongside your assigned textbook. Chapter numbers differ between editions, so find refraction and refractive index in your own contents page. The questions below are original practice items, with deliberately simple numbers so that the reasoning stays visible.

Independent topic practice for Class 10 students. Check your textbook, examination scheme and assigned learning outcomes against the official FBISE assessment frameworks and model papers. These are original exercises, not an official answer key or a predicted examination paper.

What you will practise

• Start with the boundary and normal
• Use refractive index correctly
• Apply Snell’s law
• Recognise normal incidence and apparent depth
• Write a reasoned short answer

Start with the boundary and normal

Draw the boundary between the two media as a straight horizontal line. At the point where the ray reaches it, draw a perpendicular dotted line called the normal. Label the incoming ray and outgoing ray. Measure both the angle of incidence, i, and the angle of refraction, r, from the normal. An angle measured from the surface is the complement of the angle required in Snell’s law.

Refraction occurs because light travels at different speeds in different media. At oblique incidence, entry into a medium with a higher refractive index produces bending towards the normal. Entry into a lower-index medium produces bending away from the normal. Optical density here concerns refractive index; it is not a statement about mass per unit volume.

Use refractive index correctly

The absolute refractive index is n = c/v, where c is the speed of light in vacuum and v is its speed in the material. Both speeds must use the same units, so n has no unit. If v = 2.0 × 10^8 m/s, then n = 1.5 when c = 3.0 × 10^8 m/s. A larger n means a smaller light speed in that medium.

At a boundary, frequency remains unchanged. Wavelength changes because v = fλ. If speed decreases while frequency stays fixed, wavelength decreases too. This explains why “speed and frequency both decrease” is a tempting but incorrect answer.

Apply Snell’s law

For two transparent media, n₁ sin i = n₂ sin r. The familiar ratio sin i/sin r is approximately the refractive index of the second medium only when the first medium is air, with refractive index taken as approximately 1. State that assumption rather than treating the ratio as universal.

Before using a calculator, predict whether r should be smaller or larger than i. Use degree mode for angles given in degrees. If the calculation gives sin r greater than 1, recheck the direction of travel and the indices. Under appropriate conditions this can indicate total internal reflection, rather than an ordinary refracted ray.

Recognise normal incidence and apparent depth

At normal incidence, i = 0° and the ray does not change direction. Its speed and wavelength can still change. Therefore “no bending” does not mean “no change in speed.” This distinction is useful in both short answers and MCQs.

For an object in water viewed nearly vertically from air through a plane surface, apparent depth is approximately real depth divided by the refractive index of water relative to air. The approximation depends on near-normal viewing. Do not use it without checking the viewing arrangement.

Write a reasoned short answer

If asked why a ray bends towards the normal, identify the direction of travel, compare the refractive indices and then state the bending direction. For example: the ray enters glass from air; glass has a higher refractive index, so light slows and the ray bends towards the normal at oblique incidence.

For a diagram question, arrows matter. Two unlabelled lines crossing a surface do not communicate which medium the ray entered first. Include the normal, i, r and medium names. Keep the normal distinct from the rays and use a ruler for the boundary.

Worked examples and model answers

1. Speed in glass

Glass has n = 1.50. Find the light speed.

v = c/n = (3.0 × 10^8)/1.50 = 2.0 × 10^8 m/s. The result is less than c, as expected.

2. Angle in glass

Light passes from air into glass of n = 1.50 at i = 30°. Find r.

sin r = sin 30°/1.50 = 0.3333. Therefore r ≈ 19.5°. The smaller angle confirms bending towards the normal.

3. Apparent depth

A coin lies 12 cm below water with n = 4/3. Estimate its apparent depth from air.

Apparent depth ≈ 12 ÷ (4/3) = 9 cm for near-normal viewing. The coin appears shallower.

Practice MCQs

Attempt all six before opening the answers. Write a reason beside each choice so that a correct guess is not mistaken for understanding.

1. Angles in Snell’s law are measured from the:

1. surface
2. normal
3. ray extension only
4. container base

Answer and explanation

B. normal The normal is perpendicular to the boundary.

2. The unit of refractive index is:

1. m/s
2. degree
3. none
4. metre

Answer and explanation

C. none It is a ratio of two speeds.

3. At a stationary boundary, which remains unchanged?

1. speed
2. wavelength
3. frequency
4. direction always

Answer and explanation

C. frequency Frequency is fixed by the source.

4. A higher refractive index means:

1. higher light speed
2. lower light speed
3. greater frequency always
4. no refraction

Answer and explanation

B. lower light speed n = c/v.

5. At normal incidence the ray:

1. must bend
2. does not bend
3. must stop
4. changes frequency

Answer and explanation

B. does not bend Both incidence and refraction angles are zero.

6. For air to glass at oblique incidence, the ray bends:

1. towards the normal
2. away from the normal
3. along the surface always
4. back to the source

Answer and explanation

A. towards the normal Glass normally has a higher refractive index than air.

Written self-check

1. Find n if v = 2.4 × 10^8 m/s.
2. Explain why a ray can keep its direction while its wavelength changes.
3. For air to a material of n = √2, find r when i = 45°.
4. Draw a ray passing from glass into air at an angle below the critical angle.

Suggested answers

1. n = 1.25.
2. At normal incidence there is no bending, but a change in speed at constant frequency changes wavelength.
3. sin r = sin 45°/√2 = 0.5; r = 30°.
4. The refracted ray should be farther from the normal than the incident ray.

Use your mistakes to choose the next task

Mark the MCQs only after completing the written self-check. If you chose the correct answer but cannot explain it, return to the relevant heading and write a two-sentence explanation in your own words. If a calculation went wrong, identify whether the problem came from the starting relationship, the substitution, the arithmetic or the unit. That gives you a specific correction to practise.

On your next attempt, change the order of the questions and keep the answers covered. Explain one idea aloud, then answer one question on paper without consulting the notes. A successful immediate retry is useful, but a second correct attempt on a different day gives better evidence that you can recall and apply the idea independently.

Further study

Use the official FBISE framework and model-paper page to select the subject, level and scheme that apply to you. Match the learning outcomes with your assigned textbook before deciding how much detail to revise.

More practice on this blog: Earlier Physics MCQ practice.