Is this formula given in the exam?

No. SPM Physics papers provide no formula sheet, so this must be recalled.

Which is bigger, real depth or apparent depth?

The real depth is always larger. A submerged object looks shallower than it truly is, so the apparent depth is smaller. That is why n = real depth / apparent depth is always greater than 1, a value below 1 would mean the object looks deeper, which does not happen.

Do the two depths need the same unit?

Yes. Because the refractive index is a pure ratio, the units cancel only if both depths use the same unit. Keep both in centimetres or both in metres; do not mix centimetres with metres or the ratio will be wrong by a factor of 100.

Is this the same n as in Snell’s law?

Yes, it is the same refractive index of the medium, just measured a different way. Snell’s law uses angles (n = sin i / sin r), while this method uses depths (n = real / apparent). Both should give the same value for the same material.

Refractive index by depth Formula, SPM Physics

Refractive index by depth

n = real depth / apparent depth

Not given in the exam, recall it.

What it is for

Refractive index by depth is used in Light and Optics (SPM Physics Form 4). Keep the SI units in every line of working. Light and Optics

Symbols and SI units

Symbol	Meaning	SI unit
`n`	refractive index (no unit, ratio)	,
`real depth`	real depth	m
`apparent depth`	apparent depth	m

Rearrangements

real depth = n × apparent depth
apparent depth = real depth / n

Worked example

A coin in water has real depth = 8.0 cm and apparent depth = 6.0 cm. n = real depth / apparent depth = 8.0 / 6.0 = 1.33.

Common trap

Real depth is always greater than apparent depth (the object looks shallower). Use the same unit for both depths.

Understanding the depth method

This relationship, n = real depth / apparent depth, finds the refractive index from how much shallower a submerged object looks. n is the refractive index, a ratio with no unit. The real depth is the true depth of the object and the apparent depth is where it seems to be; both are lengths, usually in centimetres or metres (m), and must share the same unit.

Light from the object bends away from the normal as it leaves the denser medium, so rays reaching the eye appear to come from a point closer to the surface. The denser the medium, the larger this effect and the larger n.

Rearrange as needed: real depth = n × apparent depth or apparent depth = real depth / n.

A worked example, step by step

A mark at the bottom of a glass block has a real depth of 9.0 cm. The glass has refractive index n = 1.5.

Find the apparent depth seen from directly above.

Rearrange the relationship to make apparent depth the subject:

apparent depth = real depth / n = 9.0 cm / 1.5 = 6.0 cm.

So the mark appears to be at 6.0 cm (2 significant figures) below the surface, which is shallower than its true 9.0 cm. This matches everyday experience: the bottom of a swimming pool looks closer than it really is.

Both depths stay in centimetres because the refractive index is a pure ratio.

Common mistakes and how this is tested

The trap is remembering which depth is larger. The real depth is always greater than the apparent depth, so n = real / apparent is always greater than 1.

Writing the ratio upside down gives a value less than 1, which is impossible for a refractive index.

Other mistakes: using different units for the two depths; assuming the object looks deeper rather than shallower; and confusing this depth method with Snell’s law (both give n, but from different measurements).

Under calculate show n = real depth / apparent depth and keep both depths in the same unit. Under explain you may need to say why the object looks shallower, linking it to rays bending away from the normal on leaving the denser medium.

Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)

Written by the spmphysics.com.my editorial team.· Updated 5 Sept 2026