Question

figure 1 shows a convex lens. match the term on the left with the appropriate location on the right.
write a short answer to each of these questions.

1. (a) principal focus (i) w

(b) optical centre (ii) x
(c) principal axis (iii) y
(d) secondary principal focus (iv) z (13.1) 5

Explanation:

Step1: Recall Convex Lens Terms

- **Principal Focus (a)**: For a convex lens, the principal focus is a point where parallel rays converge. In the diagram, \( Z \) is on the left, but the secondary principal focus (for convex lens, both sides have foci; here, the focus on the right side for the left - coming rays? Wait, no: For a convex lens, the principal focus (primary or secondary) - the point where parallel rays to the principal axis converge. The right - side focus (for rays coming from left parallel to axis) is \( X \)? Wait, no, let's re - identify:
- **Optical Centre (b)**: The optical centre of a lens is the point through which a ray passes without deviation. In the diagram, \( W \) is the center of the lens (on the principal axis, middle point), so optical centre (b) matches \( W \) (i).
- **Principal Axis (c)**: The principal axis is the line passing through the optical centre and the principal foci. The horizontal line through \( W \) and \( X \), \( Z \) is the principal axis, so principal axis (c) matches \( Y \)? Wait, no, the principal axis is the horizontal line (the line with \( W \), \( X \), \( Z \)). Wait, the terms:
- (a) Principal focus: The point where parallel rays to principal axis converge. For convex lens, if rays come from left parallel to axis, they converge at \( X \)? No, wait, in the diagram, \( Z \) is on the left, \( X \) on the right. Wait, the correct matches:
- (a) Principal focus: The focus on the right side (for convex lens, when rays come from left parallel to axis, they meet at the principal focus on the right). But in the options, (a) principal focus should match \( X \)? No, wait the left terms: (a) principal focus, (b) optical centre, (c) principal axis, (d) secondary principal focus.
- (i) \( W \), (ii) \( X \), (iii) \( Y \), (iv) \( Z \).
- Let's re - define:
- Optical Centre (b): The center of the lens, which is \( W \), so (b) optical centre matches (i) \( W \).
- Principal Axis (c): The line passing through optical centre and foci, the horizontal line (the line with \( W \), \( X \), \( Z \)), so principal axis (c) matches (iii) \( Y \)? Wait, \( Y \) is the angle? No, maybe the principal axis is the horizontal line, so (c) principal axis matches the line (but the options are points). Wait, maybe:
- (a) Principal focus: The focus on the right side, so \( X \) (ii).
- (b) Optical centre: \( W \) (i).
- (c) Principal axis: The horizontal line, but the points: the principal axis is the line through \( W \), so maybe (c) principal axis matches \( Y \)? No, \( Y \) is an angle? Wait, the correct matches are:
- (a) Principal focus: \( X \) (ii)
- (b) Optical centre: \( W \) (i)
- (c) Principal axis: \( Y \)? No, maybe the principal axis is the line, but the options are points. Wait, the principal axis is the horizontal line (the line containing \( W \), \( X \), \( Z \)), so (c) principal axis corresponds to the line, but the options are points. Wait, maybe the principal axis is represented by the line, and \( Y \) is the angle? No, perhaps I made a mistake. Let's use the standard definitions:
- **Optical Centre (b)**: The point at the center of the lens, so \( W \) (i). So (b) - (i).
- **Principal Focus (a)**: For a convex lens, the principal focus (primary) is the point where parallel rays to the principal axis converge. If the lens is convex, and rays come from the left parallel to the principal axis, they converge at \( X \) (ii). So (a) - (ii).
- **Principal Axis (c)**: The line passing through the optical centre and the principal foci, which is the horizontal line (the line with \( W \), \( X \), \( Z \)), so the principal axis is the line, and the point related? Wait, the principal axis is the line, so (c) principal axis corresponds to \( Y \)? No, \( Y \) is an angle. Wait, maybe \( Y \) is the principal axis? No, the principal axis is horizontal. Wait, the correct matches are:
- (a) Principal focus: \( X \) (ii)
- (b) Optical centre: \( W \) (i)
- (c) Principal axis: \( Y \)? No, maybe the principal axis is the line, and the option (iii) \( Y \) is the principal axis? No, I think I messed up. Let's start over:
- **Optical Centre (b)**: The center of the lens, which is \( W \), so (b) - (i).
- **Principal Axis (c)**: The line passing through optical centre and foci, the horizontal line (so the line with \( W \), \( X \), \( Z \)), so (c) - (iii) \( Y \)? No, \( Y \) is an angle. Wait, the principal axis is the horizontal line, so the point - maybe the principal axis is represented by the line, and the option (iii) \( Y \) is the principal axis? No, perhaps the principal axis is the line, and the answer is:
- (a) Principal focus: \( X \) (ii)
- (b) Optical centre: \( W \) (i)
- (c) Principal axis: \( Y \) (iii) (assuming \( Y \) is the principal axis, maybe the label is mis - placed)
- (d) Secondary principal focus: \( Z \) (iv) (since secondary principal focus is on the left side for convex lens, when rays come from right parallel to axis, they meet at \( Z \))

Step2: Match Each Term

- (a) Principal focus: The focus on the right side (for convex lens, where parallel rays from left converge), so matches (ii) \( X \).
- (b) Optical centre: The center of the lens, which is \( W \), so matches (i) \( W \).
- (c) Principal axis: The line passing through optical centre and foci (horizontal line), so matches (iii) \( Y \) (assuming \( Y \) is the principal axis, maybe the label is for the axis).
- (d) Secondary principal focus: The focus on the left side (for convex lens, where parallel rays from right converge), so matches (iv) \( Z \).

Answer:

(a) - (ii) \( X \)
(b) - (i) \( W \)
(c) - (iii) \( Y \)
(d) - (iv) \( Z \)