(a) An object is placed in front of a convex lens of focal length f. If the distance of the object from the…
(a) An object is placed in front of a convex lens of focal length f. If the distance of the object from the lens is 2f, draw a ray diagram to show the formation of the image. Write the value of magnification in this case.
(b) A student has focussed the image of a candle flame on a white screen using a convex lens. The situation is as given below :
Length of the flame = 2 cm
Focal length of the lens = 12 cm
Distance of the flame from the lens = 16 cm
If the flame is perpendicular to the principal axis of the lens, calculate the values of the following :
(i) Distance of the image from the lens
(ii) Length of the image formed
Solution
(a)
[ray diagram: object AB placed beyond 2F1, converging lens M, image A'B' formed between F2 and 2F2, rays traced through O, F1, 2F1, C1 and F2, 2F2, C2]
(Deduct ½ mark for not marking arrows)
Magnification = -1
(b) (i) u = – 16 cm; f : + 12 cm
Formula $\dfrac{1}{v}$ - $\dfrac{1}{u}$ = $\dfrac{1}{f}$
Substitution Result $\dfrac{1}{v}$ = $\dfrac{1}{u}$ + $\dfrac{1}{f}$ = 1/(-16 cm) + 1/(12 cm) = +1/(48 cm)
or V = + 48 cm or v = + 48 cm
(Award full marks if data not written but calculations are correct)
(iv) hi = v/u × h0
= (+48 cm / -16 cm) × 2 cm
= – 6 cm
Image is 6 cm in size.