Light: Mirrors and Lenses

Given: Angle of incidence (angle between incident ray and normal) = 40°

Concept used: By the first law of reflection, the angle of incidence equals the angle of reflection. The angle made by a ray with the mirror = 90° − (angle made with the normal).

Working:
- Angle of reflection = angle of incidence = 40°
- Angle made by the reflected ray with the mirror = 90° − 40° = 50°

Answer: Option (ii) 50°

Concept used: By the laws of reflection:
1. Angle of incidence (i) = Angle of reflection (r), both measured from the normal.
2. The incident ray, normal, and reflected ray all lie in the same plane.

Case (i): Light ray falls along the normal
- The angle of incidence = 0° (ray is along the normal).
- Therefore, angle of reflection = 0°.
- The reflected ray travels back along the same path as the incident ray (i.e., along the normal, but in the opposite direction).
- Angle of reflection = 0°

Case (ii): Mirror is tilted, but the light ray still falls along the normal to the tilted surface
- Even though the mirror is tilted, the ray still falls along the normal, so the angle of incidence = 0°.
- Therefore, angle of reflection = 0°.
- The reflected ray again travels back along the same path as the incident ray.
- Angle of reflection = 0°

Case (iii): Mirror is tilted, and the light ray falls at an angle of 20° from the normal
- Angle of incidence = 20°.
- By the law of reflection, angle of reflection = 20°.
- Draw the normal at the point of incidence on the tilted mirror. Using a protractor, draw the reflected ray on the other side of the normal such that it makes an angle of 20° with the normal.
- Angle of reflection = 20°

*(Note: Use a ruler and protractor to draw the diagrams accurately as instructed. The reflected ray is always on the opposite side of the normal from the incident ray, making an equal angle.)*

Concept used:
- A plane mirror always forms an image that is erect and of the same size as the object.
- A convex mirror always forms an image that is erect and smaller (diminished) than the object.
- A concave mirror (when the object is close) forms an image that is erect and larger (enlarged) than the object.

Matching:

| Image | Mirror |
|---|---|
| (i) — erect image, same size as object | Plane mirror |
| (ii) — erect image, smaller than object | Convex mirror |
| (iii) — erect image, larger than object | Concave mirror |

Answer: Image (i) → Plane mirror; Image (ii) → Convex mirror; Image (iii) → Concave mirror.

Concept used:
- A flat transparent glass piece does not bend light; the object appears the same size and shape.
- A convex lens (converging lens), when the object is placed close, forms an erect and enlarged image.
- A concave lens (diverging lens) always forms an erect and diminished (smaller) image.

Matching:

| Image | Lens/glass type |
|---|---|
| (i) — erect image, same size as object | Flat transparent glass piece |
| (ii) — erect image, larger (enlarged) than object | Convex lens |
| (iii) — erect image, smaller (diminished) than object | Concave lens |

Answer: Image (i) → Flat transparent glass piece; Image (ii) → Convex lens; Image (iii) → Concave lens.

Given: Light is incident along the normal to the mirror.

Concept used: The angle of incidence is measured between the incident ray and the normal at the point of incidence. If the ray travels along the normal, the angle between the ray and the normal is 0°.

Working:
- Angle of incidence = 0° (since the ray is along the normal).
- By the law of reflection, angle of reflection = angle of incidence = 0°.
- The reflected ray travels back along the normal (same path, opposite direction).
- Reflection does take place.

Answer: Option (ii) Angle of incidence is 0°

Concept used:
- A plane mirror reflects the graph sheet image with squares of the same size — the image is neither enlarged nor diminished.
- A concave mirror (when the graph sheet is close) forms an enlarged image — the squares appear bigger.
- A convex mirror always forms a diminished image — the squares appear smaller and more squares are visible.

Identification (based on the images seen in Fig. 10.25):
- The mirror showing the graph squares of the same size → Plane mirror
- The mirror showing the graph squares larger (enlarged) → Concave mirror
- The mirror showing the graph squares smaller (diminished, more squares visible) → Convex mirror

*(Note: Since the actual figure cannot be seen, the identification is based on the standard properties of the three mirrors as described above.)*

Given: A woman is walking towards a large concave mirror, i.e., she starts far away and moves closer.

Concept used: For a concave mirror:
- When the object is far away, the image is inverted and small (diminished).
- As the object moves closer, the inverted image grows larger.
- When the object comes very close (within the focal length), the image becomes erect and magnified.

Working:
- Starting from a large distance: image is inverted and diminished.
- As she walks closer: the inverted image keeps getting larger (magnified).
- When she is very close to the mirror (closer than the focal point): the image becomes erect and magnified.

Answer: Option (iii) her inverted image keeps increasing in size and eventually it becomes erect and magnified.

Observation:
- When the magnifying glass is held close to the text (within its focal length), the letters appear erect and enlarged (bigger than they are written).
- As the magnifying glass is moved farther away from the text, the letters first appear very large and then, beyond a certain distance, the image becomes inverted and diminished.

Explanation:
- A magnifying glass is a convex lens (converging lens).
- When the object (text) is placed within the focal length of a convex lens, it acts as a magnifier and produces an erect, enlarged, virtual image.
- As the distance increases beyond the focal length, the image becomes real, inverted, and changes in size.

Answer: A magnifying glass is a convex lens. When held close to the text, it produces an enlarged, erect image. As it is moved away, the image eventually becomes inverted.

Concept used:
- Concave mirror: Its reflecting surface curves inwards. It can form erect enlarged images (when object is close) or inverted images (when object is far).
- Convex mirror: Always forms erect and diminished images.
- Convex lens: When the object is placed at a sufficient distance, the image becomes inverted. (It is a converging lens.)
- Concave lens: Always forms erect and diminished images. (It is a diverging lens.)

Matching:

| Column I | Column II |
|---|---|
| (i) Concave mirror | (a) Spherical mirror with a reflecting surface that curves inwards. |
| (ii) Convex mirror | (b) It forms an image which is always erect and diminished in size. |
| (iii) Convex lens | (c) Object placed behind it may appear inverted at some distance. |
| (iv) Concave lens | (d) Object placed behind it always appears diminished in size. |

Answer: (i)→(a), (ii)→(b), (iii)→(c), (iv)→(d)

Analysis of Assertion: Convex mirrors are indeed preferred as side-view (rear-view) mirrors in vehicles because they always form erect images and cover a wider field of view. → Assertion is correct.

Analysis of Reason: A convex mirror, due to its outward-curving surface, diverges the reflected light rays. This allows it to capture a much wider area of the road behind compared to a plane mirror of the same size. → Reason is correct.

Link between Assertion and Reason: The reason that convex mirrors provide a larger view area is precisely why they are preferred for observing traffic behind — the wider field of view is the direct explanation for their use as rear-view mirrors.

Answer: Option (i) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

Concept used:
- A concave mirror can form an erect and enlarged image when the object is placed close to it.
- A convex mirror always forms an erect and diminished (smaller) image regardless of the object's distance.
- A plane mirror always forms an erect image of the same size as the object.

Analysis of figures (based on standard NCERT depiction for this question):
- Figure (a): The image I is shown as erect and larger than the object O → This is the behaviour of a concave mirror (object placed close).
- Figure (b): The image I is shown as erect and smaller than the object O → This is the behaviour of a convex mirror.

Answer: Option (iii) Figure (a) indicates a concave mirror and Figure (b) indicates a convex mirror.

Observation:
- When the pencil is placed behind the empty glass tumbler, it appears normal (same size and shape).
- When the tumbler is filled halfway with water and the pencil is viewed through the water portion, the pencil appears bent or broken at the water surface, and the part of the pencil seen through the water appears thicker/wider (magnified) compared to the part seen above the water.

Explanation:
- The cylindrical glass tumbler filled with water acts like a convex (converging) lens due to its curved surface.
- When light from the pencil passes from water (a denser medium) into air (a less dense medium) through the curved surface of the tumbler, it bends (refracts).
- This bending of light at the curved water–glass–air boundary causes the pencil to appear distorted — the submerged part looks wider or displaced compared to the part above water.
- The curved surface of the water-filled tumbler converges the light rays, making the pencil appear magnified in the region seen through the water.

Conclusion: The apparent change in the shape of the pencil is due to refraction of light at the curved surface of the water-filled glass tumbler, which acts as a convex lens.