Chapter 10: Light: Mirrors and Lenses

Given. The angle of incidence, measured from the incident ray to the normal, is $$\angle i = 40^{\circ}$$.

Step 1 — Law of reflection. By the law of reflection, the angle of reflection (measured from the reflected ray to the normal) equals the angle of incidence. Hence

Step 2 — Angle with the mirror. The normal is drawn perpendicular to the mirror, so the angle between the normal and the mirror surface is $$90^{\circ}$$. The angle the reflected ray makes with the mirror is therefore

Hence the correct option is (ii) $$50^{\circ}$$.

We identify each mirror by the size and orientation of the image it makes of the cap:

• Plane mirror. A plane mirror forms an image of exactly the same size as the object and erect (upright). So the image labelled with a cap of the same size as the real one and standing upright corresponds to the plane mirror.
• Convex mirror. A convex mirror always forms an image that is erect and smaller (diminished) than the object. So the image showing a smaller upright cap corresponds to the convex mirror.
• Concave mirror. When an object is placed close to a concave mirror (within its focal length, as with the sketch-pen cap held in front of it), the image is erect and larger (magnified). So the image showing an enlarged upright cap corresponds to the concave mirror.

Reading the standard NCERT figure 10.23 from left to right — same-size image, smaller image, larger image — gives the matching below.

We identify each optical piece by what happens to the size of the cap seen through it:

• Flat transparent glass piece. A plane sheet of glass does not converge or diverge the light, so the cap looks the same size and erect through it.
• Convex lens. A convex lens is a converging lens. When the cap is placed close to it (within one focal length), it acts like a magnifying glass and produces an erect, magnified image. So the enlarged image belongs to the convex lens.
• Concave lens. A concave lens is a diverging lens; it always produces an erect, diminished (smaller) image of the object. So the smaller image belongs to the concave lens.

Matching the three images in Fig. 10.24 by size — same size, larger, smaller — with the three optical pieces:

The angle of incidence is defined as the angle between the incident ray and the normal. If the light travels along the normal, the incident ray and the normal are the same line, so

By the law of reflection $$\angle r = \angle i = 0^{\circ}$$, so the reflected ray also lies along the normal (it retraces its path). Reflection does take place — it is not zero. Therefore only option (ii) is correct.

Look at how the graph-sheet squares appear in the image formed by each mirror.

• Plane mirror. The squares of the graph sheet are seen with the same size as on the actual sheet, and the lines remain straight. Any distortion or change of size means the mirror is not plane.
• Concave mirror. A concave mirror is a converging mirror. When the graph sheet is held close to it, the image of the sheet is magnified — the squares look larger than on the actual sheet.
• Convex mirror. A convex mirror is a diverging mirror. It always makes objects look smaller, so the squares of the graph sheet appear diminished in its image, and a larger area of the sheet can be seen than the size of the mirror.

Rule for labelling in Fig. 10.25: above the mirror whose image shows same-size squares, write “Plane mirror”; above the mirror whose image shows larger squares, write “Concave mirror”; above the mirror whose image shows smaller squares, write “Convex mirror”.

Behaviour of a large concave mirror as the object approaches it:

• When the woman is far away from the concave mirror (well beyond its focal point), the mirror forms a real, inverted image of her. As she walks closer, this inverted image grows larger and larger.
• When she crosses the focal point of the mirror and comes very close to it, the image becomes virtual, erect and magnified (this is exactly why a concave mirror is used as a shaving/make-up mirror).

So as she walks in, first she sees an inverted image that keeps growing in size, and finally, close to the mirror, the image flips to being erect and magnified. That description matches option (iii).

Options (i) and (iv) claim an erect image throughout, which is wrong because a large concave mirror shows an inverted image at large distances. Option (ii) says the inverted image keeps decreasing, which is the opposite of what happens as she approaches.

What we observe.

• When the magnifying glass is held close to the text (within a certain small distance, less than its focal length), the letters appear larger and erect. This distance is the useful range of a magnifier.
• As we slowly move the lens away from the text, the letters keep looking larger for a while, then at one particular distance they suddenly become blurred and finally, on moving still further, the letters look inverted and their size begins to decrease.

Why this happens. As long as the text is between the lens and its focal point, the lens forms a virtual, erect, magnified image (magnifying-glass action). When the text goes beyond the focal point, a real, inverted image is formed on the other side of the lens; that is what our eye sees as an upside-down image at large distance.

Type of lens. A magnifying glass converges light and produces a magnified erect image, so it is a convex lens (a converging lens).

Take each item of Column I and match by definition/behaviour:

• (i) Concave mirror → (a). A concave mirror is defined as a spherical mirror whose reflecting surface curves inwards (like the inside of a spoon). This is a pure definition, so it matches (a).
• (ii) Convex mirror → (b). A convex mirror is a diverging spherical mirror. Whatever the position of the object in front of it, the image is virtual, erect and diminished, which is exactly statement (b).
• (iii) Convex lens → (c). A convex (converging) lens forms a real, inverted image when the object is placed beyond its focal length. So looking through the lens at an object placed at a suitable distance behind it, one sees an inverted image — matching (c).
• (iv) Concave lens → (d). A concave (diverging) lens always forms a virtual, erect, diminished image, no matter where the object is placed. So it corresponds to (d).

Is the Assertion true? Yes. Rear-view mirrors of vehicles are indeed convex mirrors. A convex mirror always produces an erect image and covers a wide field of view, so the driver can see traffic on a large stretch of road behind the vehicle.

Is the Reason true? Yes. Because a convex mirror bulges outward, rays coming from a wide range of directions can hit it and get reflected towards the driver's eyes. Compared with a plane mirror of the same size, a convex mirror shows a much larger area of the scene — this is the well-known “wider field of view” of a convex mirror.

Does the Reason correctly explain the Assertion? Yes. The very reason we prefer convex mirrors as rear-view mirrors is that they let us see a much larger area of the road behind us than a plane mirror would. So Reason directly explains the Assertion.

Hence option (i) is correct.

We identify each mirror from the position (and size) of the image $$I$$ relative to the object $$O$$ and the mirror $$M$$.

Figure (a). The image $$I$$ appears at the same distance behind the mirror as the object $$O$$ is in front of it, and the arrow representing $$I$$ has the same height as the arrow representing $$O$$ (image of same size, erect). This is exactly the property of a plane mirror:

Figure (b). The image $$I$$ is again behind the mirror and erect, but its distance from $$M$$ is smaller than the distance of $$O$$ from $$M$$. So the image lies between the pole of the mirror and where a plane-mirror image would sit, and it is diminished. Only a convex mirror forms such a virtual, erect image that lies between its pole and its focal point behind the mirror.

A concave mirror, in contrast, would produce either a real inverted image in front of the mirror (for distant objects) or a virtual, magnified image whose apparent position lies farther behind the mirror than the object is in front — neither of which matches (a) or (b).

Therefore Figure (a) is a plane mirror and Figure (b) is a convex mirror — option (iv).

Observation. With the tumbler empty (Fig. 10.28a) we see the pencil almost as it really is — a single straight rod behind the glass. When the tumbler is filled halfway with water (Fig. 10.28b), the pencil looks broken at the water surface: the part seen through water appears shifted sideways and often thicker/larger than the part seen above the water level (which is viewed only through air and glass).

Explanation. Light rays travel from the pencil to our eyes. They pass through different media on the way:

• The upper half of the tumbler contains only air, so the light from the top part of the pencil is only slightly bent by the thin curved glass and reaches our eyes almost undeviated.
• The lower half of the tumbler is filled with water. Light rays coming from the lower part of the pencil first enter water, then pass through the curved glass wall, then into air, before reaching our eyes.

Whenever light travels from one transparent medium to another of different optical density, it bends at the boundary. This bending is called refraction. Water is optically denser than air, so a ray of light passing from water to air (through the glass) is refracted — it changes direction.

Because the curved water-filled portion of the tumbler acts like a cylindrical convex lens, all the light coming from the submerged part of the pencil is bent inwards, giving a magnified, laterally shifted image of that portion. The part above the water is not refracted this way, so it appears in its original position and size. The mismatch between the two portions is what makes the pencil look bent, broken or thicker at the water level.

So the pencil's shape has not really changed — the change is only in the direction of the light rays reaching our eyes, caused by refraction at the water and the curved glass surfaces.