Real and Apparent Depth: μ = Real Depth ÷ Apparent Depth, Shift and the Bent Stick (ICSE Class 10)

Understand Real and Apparent Depth

Real and Apparent Depth: formulas and key facts

Refractive index from depths

$\mu =\frac{\text{real depth}}{\text{apparent depth}}$

Viewing from nearly directly above.

Apparent depth

$\text{apparent depth}=\frac{\text{real depth}}{\mu }$

Water: three quarters; glass (1.5): two thirds.

Shift (apparent rise)

$\text{shift}=\text{real depth}\left(1-\frac{1}{\mu }\right)$

Larger for deeper objects and larger μ.

How to solve Real and Apparent Depth questions

1. 1Measure every depth from the surface the observer looks through.
2. 2If the shift (rise) is given, find the apparent depth first: apparent = real − shift.
3. 3Use $\mu =\frac{\text{real}}{\text{apparent}}$, rearranged as needed.
4. 4For a bubble in a block seen from both faces, use real depth from top + real depth from bottom = thickness.
5. 5Give every depth with its unit (cm or m).

Real and Apparent Depth in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Tricks to remember Real and Apparent Depth

Short memory aids. Say each one aloud once, then use it on a question the same day.

• Real over Apparent, R over A

  μ = Real ÷ Apparent: 'Really Above' reminds you that the real depth is on top of the fraction.

  Use it when: Not inverting the formula.

• Three quarters for water, two thirds for glass

  Water hides a quarter of the depth; glass hides a third.

  Use it when: Quick estimates and checks.

• Violet looks closer

  Higher μ (violet) means a smaller apparent depth: 'violet very near, red really deep'.

  Use it when: Colour questions.

• Away on the way out

  Light leaving water bends away from the normal, so the image rises; light entering water bends towards it, so a bird looks higher.

  Use it when: Ray diagrams and the fish's view.

Real and Apparent Depth: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Where students lose marks in Real and Apparent Depth

The slips examiners see most often, and what to write instead.

• ✗Mistake: Inverting the ratio

  μ = real ÷ apparent, and μ > 1, so the apparent depth is always the smaller one.

  Wrong working

  Real depth 12 cm, μ 1.5: apparent depth $=12\times 1.5=18$ cm.

  Right working

  Apparent depth $=\frac{12}{1.5}=8$ cm.

  ✓Do this: Check that the apparent depth is less than the real depth.

  Usually costs: The answer mark.

• ✗Mistake: Leaving out the unit

  A depth without a unit is incomplete.

  Wrong working

  'Real depth = 6.'

  Right working

  'Real depth = 6 cm.'

  ✓Do this: Write the unit on every depth.

  Usually costs: Reported by CISCE examiners for 2025 Q4(ii).

• ✗Mistake: Mishandling a block turned upside down

  Turning the block over changes the real depth measured from the viewing face, so the apparent depth changes too.

  Wrong working

  'The bubble appears at the same depth from either face.'

  Right working

  'From the other face, real depth = thickness − first real depth; divide by μ again.'

  ✓Do this: Always measure depths from the face you look through.

  Usually costs: Reported for 2025 Q4(ii), where candidates did not link a change in real depth to apparent depth.

• ✗Mistake: Drawing all lines solid in the ray diagram

  Only real rays are solid with arrows; the backward extensions to the image are dashed.

  Wrong working

  Emergent rays traced back with solid lines and no arrows.

  Right working

  Solid rays with arrows from object to eye; dashed extensions to the image.

  ✓Do this: Arrows on every real ray; dashes for virtual extensions.

  Usually costs: Diagram marks.

Practice questions on Real and Apparent Depth

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQBoard level

   Which relation is correct for viewing from directly above?
   (a) $\mu =\frac{\text{apparent depth}}{\text{real depth}}$
   (b) $\mu =\frac{\text{real depth}}{\text{apparent depth}}$
   (c) $\mu =\text{real depth}-\text{apparent depth}$
   (d) $\mu =\text{real depth}\times \text{apparent depth}$

   Hint

   μ must be greater than 1.

   Answer

   (b) $\mu =\frac{\text{real depth}}{\text{apparent depth}}$

2. Q2 · 3 marks · Short answerHarder board level

   Describe, as you would draw it, the ray diagram that explains why a straight stick, held slanting with its lower half under water, looks bent where it meets the water.

   Hint

   Take the lower tip of the stick as the object.

   Answer

   Take the lower tip A of the stick under water. Draw two rays from A to the surface; on leaving the water each bends away from the normal and enters the eye. Extending the emergent rays backwards (dashed), they meet at A′, above A. Every immersed point is raised in this way, the deeper ones most, so the immersed part appears along the line from the surface point to A′: bent upward and shorter.

3. Q3 · 1 mark · Very short answerBoard level

   A coin at the bottom of a vessel holding 36 cm of a liquid appears to be 27 cm below the surface. Find the refractive index of the liquid.

   Hint

   Real ÷ apparent.

   Answer

   $\mu =\frac{36}{27}=\frac{4}{3}\approx 1.33$.

4. Q4 · 2 marks · Short answerHarder board level

   A small object lies on the floor of a pool. In which colour of light would it appear (a) nearest the surface, (b) deepest? Explain.

   Hint

   μ is larger for shorter wavelengths.

   Answer

   (a) Violet, (b) red. Apparent depth = real depth ÷ μ, and μ of water is greatest for violet and least for red.

5. Q5 · 2 marks · Short answerHarder board level

   An ink dot under a glass block 4.5 cm thick appears to be raised by 1.5 cm when viewed from above. Find the refractive index of the glass.

   Hint

   Find the apparent depth first.

   Answer

   Apparent depth $=4.5-1.5=3$ cm; $\mu =\frac{4.5}{3}=1.5$.

6. Q6 · 3 marks · Short answerHarder board level

   A beaker is filled with oil to a depth of 21 cm. A coin at the bottom appears to be raised by 7 cm. (a) Find the refractive index of the oil. (b) If half the oil is poured out, what is the new shift?

   Hint

   The shift is proportional to the real depth.

   Answer

   (a) Apparent depth $=14$ cm; $\mu =\frac{21}{14}=1.5$. (b) Real depth 10.5 cm; shift $=10.5\left(1-\frac{1}{1.5}\right)=3.5$ cm.

7. Q7 · 2 marks · Short answerHOTS / competency

   A fish just below the surface of a pond looks up at a kingfisher sitting on a branch. Does the bird appear higher or lower than it really is? Explain with reference to the bending of light.

   Hint

   Now the light travels from air into water.

   Answer

   Higher. Light from the bird bends towards the normal on entering the denser water, so the rays reaching the fish's eye, traced back, seem to come from a point above the bird.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.μ in terms of depths?Show answer

   Real depth ÷ apparent depth.

2. 2.Apparent depth of water 40 cm deep (μ = 4/3)?Show answer

   30 cm.

3. 3.Shift of a mark under a glass block 8 cm thick (μ = 1.5)?Show answer

   About 2.7 cm.

4. 4.In which colour does an underwater object look deepest?Show answer

   Red.

5. 5.Does a bird seen by a fish appear higher or lower?Show answer

   Higher.

Real and Apparent Depth: frequently asked questions