Why a Pencil Looks Bent in a Glass of Water: Refraction Explained

Drop a pencil into a glass of water and look at it from the side. The pencil seems to snap at the water’s surface, and the part underneath looks shifted and slightly fatter. Pull it out and it is perfectly straight.

Nothing happened to the pencil. What changed is the path of the light reaching your eyes. This guide explains why a pencil looks bent in water, shows how refraction obeys one simple law, and then puts a number on the illusion so you can use it in Class 10, Class 12 and entrance-exam questions.

What Your Eyes Get Wrong

Light changes direction when the medium changes

Light travels at about 3 × 10⁸ m/s in vacuum and more slowly in any material. When a ray crosses from one transparent medium into another at an angle, its speed changes, and so does its direction. This bending is called refraction of light. A ray moving from water into air speeds up and bends away from the normal, the imaginary line perpendicular to the surface.

What your brain assumes

Your brain assumes that light always reaches your eye along a straight line. Rays from the submerged part of the pencil bend at the surface before they reach you, but your brain traces them straight back, as if nothing had bent them. Those traced-back lines meet at a point higher than the real one, so the submerged part appears lifted towards the surface. Meanwhile, the part of the pencil in air is seen in its true position. The join at the surface is where the pencil seems to snap.

Why the underwater part also looks fatter

A round glass of water also behaves like a cylindrical lens. Viewed from the side, it magnifies the submerged part sideways, so it looks wider as well as shifted.

Speed, Angle and Index: The Rules Behind the Bend

Refractive index in one line

The refractive index of a medium, n = c / v, tells you how much slower light travels there than in vacuum. A higher n means a slower speed and a stronger bend.

Snell’s law

For a ray crossing from medium 1 to medium 2:

n₁ sin i = n₂ sin r

Here i is the angle of incidence and r is the angle of refraction, both measured from the normal. Three rules of thumb follow from it:

• Going into a medium with a higher n (a denser medium), the ray bends towards the normal.
• Going into a medium with a lower n (a rarer medium), the ray bends away from the normal.
• A ray travelling along the normal does not bend at all.

A quick check with numbers

A ray in air strikes water (n = 4/3) at an angle of incidence of 45°. Then sin r = sin 45° / (4/3) = 0.707 / 1.33 ≈ 0.53, so r ≈ 32°. The ray bends towards the normal, as the rule predicts. Reverse the journey, from water to air, and the ray bends away from the normal. Increase the angle enough on that reverse trip and the ray stops leaving the water at all, which is total internal reflection, a favourite exam topic.

Putting a Number on the Illusion

The apparent depth formula

When you look almost straight down into water, the bottom appears closer to the surface than it really is. For near-normal viewing:

n = real depth / apparent depth

So apparent depth = real depth / n. Water therefore always looks shallower than it is, by a factor of about 3/4.

Worked example: the coin in the tank

A coin lies 12 cm below the surface of water (n = 4/3). How deep does it appear from directly above?

Step 1: Apparent depth = real depth / n.

Step 2: = 12 / (4/3) = 12 × 3/4 = 9 cm.

The coin appears raised by 3 cm. By the same logic, a swimming pool that is 2.0 m deep looks only about 1.5 m deep from the edge.

Everyday cases of the same idea

• Fish and spears: a fish appears closer to the surface than it is, which is why a spear must be aimed below the apparent position.
• Straws and spoons: the same bend you saw in the pencil appears in a straw or spoon in a glass of juice.
• Sky effects: atmospheric refraction makes stars twinkle and lets you see the Sun slightly before it actually clears the horizon.

For more real-world examples of bending light, see everyday applications of reflection and refraction.

From Class 8 to Class 12: Where Refraction Returns

The school chapters

State Board and ICSE syllabi cover the same ideas under their own chapter titles, so check your textbook for the exact names.

In the entrance exams

• KCET: ray optics is part of the II PUC syllabus, and refractive index, apparent depth and lens questions suit the short MCQ format.
• NEET UG 2026: the NMC syllabus lists refraction at plane and spherical surfaces, the thin lens formula, the lens maker formula and total internal reflection under Optics. This guide to optics for NEET shows how the chapter is usually tested.
• JEE Main: the Optics unit covers reflection and refraction at plane and spherical surfaces, total internal reflection, prism deviation and dispersion, and the lens formula.

For JEE Advanced and for exam years after 2026, check the latest official syllabus.

Why the early years matter

Because refraction returns at every stage, a student who grasps the idea in Class 8 to 10 meets Class 12 optics as a revision, not a shock. That is the thinking behind Deeksha Vedantu’s Foundation Program for Grades 8, 9 and 10, which builds concepts in Science and Mathematics before the pressure of board and entrance exams begins.

Try It, Then Test Yourself

Three experiments with a glass of water

1. The bent pencil. Place a pencil in a glass of water and look from the side, then from directly above. Notice how the bend changes with your viewing angle.
2. The vanishing coin. Put a coin at the bottom of an opaque bowl and step back until the rim just hides it. Ask a friend to pour water in slowly. The coin reappears, because refraction lifts its apparent position above the rim.
3. Measure apparent depth. Hold a ruler upright in a tank of water, look straight down, and compare the depth you read with the real depth. The ratio should be close to 3/4.

Five questions to check yourself

1. The refractive index of glass is 1.5. What is the speed of light in it? Answer: 3 × 10⁸ / 1.5 = 2 × 10⁸ m/s.
2. A ray in air strikes glass (n = 1.5) at 30° to the normal. Find the angle of refraction. Answer: sin r = 0.5 / 1.5 = 0.333, so r ≈ 19.5°.
3. A fish is 1.2 m below the surface of water (n = 4/3). How deep does it appear? Answer: 1.2 / (4/3) = 0.9 m.
4. Does a ray bend towards or away from the normal when it passes from glass into air? Answer: away from the normal.
5. Light travels at 2.0 × 10⁸ m/s in medium A and at 2.25 × 10⁸ m/s in medium B. Which has the higher refractive index? Answer: A (n = 1.5, against 1.33 for B).

Mistakes that cost marks

• Measuring angles from the surface instead of from the normal.
• Saying that light always bends towards the normal. It depends on whether n increases or decreases.
• Writing apparent depth = real depth × n. It is real depth divided by n.
• Using the apparent depth formula for sharply oblique viewing. It holds for near-normal viewing.

For working Class 10 problems on this chapter, try these step-by-step light numericals.

Frequently asked questions

Q1. Why does a pencil look bent in water?

Light from the submerged part of the pencil bends away from the normal as it passes from water into air. Your brain traces those rays straight back, so the submerged part appears raised, and the pencil seems to bend at the surface.

Q2. Is the pencil actually bent?

No. The pencil stays perfectly straight. Only the path of the light reaching your eyes changes, which creates the illusion.

Q3. Why does water look shallower than it really is?

Refraction at the surface makes objects under water appear closer to the surface. For near-normal viewing, apparent depth equals real depth divided by the refractive index, so a bottom 12 cm deep in water appears about 9 cm deep.

Q4. Does light bend towards or away from the normal when it goes from water into air?

It bends away from the normal, because light speeds up when it moves from water, a denser medium, into air, a rarer medium.

Q5. Is refraction important for NEET, JEE and KCET?

Yes. Refraction at plane and spherical surfaces, total internal reflection, lenses and prisms are part of the optics syllabus for NEET UG 2026 and JEE Main, and ray optics is part of the KCET and board syllabi. Always check the latest official syllabus for your exam year.