A 6 cm high object is placed 43ncm from a converging lens of focal length 24 cm. Find the image’s position and draw a ray diagram approximately to scale.
To find the position of the image formed by a converging lens, we can use the lens formula:
1/f = 1/v - 1/u
where:
f = focal length of the lens
v = image distance from the lens (in cm) [positive if the image is formed on the opposite side of the object]
u = object distance from the lens (in cm) [positive if the object is on the same side as the incident light]
Given:
f = 24 cm
u = -43 cm (since the object is placed on the opposite side of the lens)
To find v, we rearrange the lens formula:
1/v = 1/f - 1/u
Substituting the values:
1/v = 1/24 - 1/(-43)
To simplify, we can rewrite -1/43 as -1/(-43/1):
1/v = 1/24 + 1/(43/1)
Now, find a common denominator:
1/v = 1/24 + 1/(43/1) * (24/24)
= 1/24 + 24/43
Combining the fractions:
1/v = (1 + (24/43)) / 24
= (43 + 24) / (43 * 24)
= 67 / (43 * 24)
To find v, take the reciprocal of both sides:
v = (43 * 24) / 67
v ≈ 15.36 cm
Therefore, the image is formed approximately 15.36 cm from the converging lens.
To draw a ray diagram, follow these steps:
1. Draw the principal axis: a horizontal line passing through the center of the lens.
2. Place the lens on the principal axis. Use an arrow or other indication to show the direction in which the light is passing through.
3. Draw the object. In this case, draw a vertical line on the left side of the lens, representing the 6 cm high object placed 43 cm from the lens.
4. To determine the path of the rays, draw two incident rays: one parallel to the principal axis and one that passes through the focal point before reaching the lens.
5. Draw the refracted rays: one that passes through the focal point on the opposite side of the lens, and one that is refracted parallel to the principal axis.
6. Extend the refracted rays until they intersect. This point of intersection represents the position of the image formed by the lens.
Please note that an approximate ray diagram cannot be drawn to scale in this text-based format. It is recommended to refer to a diagramming tool or a physics textbook for an accurate visual representation.