Read the following passage and answer the questions given : Lenses can form different types of images…
Read the following passage and answer the questions given :
Lenses can form different types of images depending upon their focal length and position of object. A convex lens can create real, inverted or virtual, erect images, while a concave lens forms only virtual and diminished images. The focal length determines the power of lens. Convex lenses have positive focal length while concave lenses have negative focal length by convention. When lenses are placed together, their combined power is determined by the sum of their individual powers. Ray diagrams help to visualize how light converges or diverges through lens to form an image.
(a) A convex lens of focal length 20 cm is used to form an image. If an object is placed at 40 cm from the lens, what will be the position and nature of image ? [1]
(b) Illustrate the formation of image with the help of ray diagram, when the object is placed between the optical centre and principal focus of concave lens. [1]
(c) (i) A lens combination consists of a convex lens of focal length 30 cm and a concave lens of focal length 15 cm placed together. Find the equivalent focal length and power of this lens combination. [2]
Solution
(a)
• Position - Image will form at 40 cm / 2F /C
• Nature – Real and inverted
/
Alternate answer
f = +20 cm, u = -40 cm
Using Lens Formula,
1 1 1
− =
v u f
1
− =
v −40 20
1
= +
v 20 −40
v = + 40 cm
Position - 40 cm on the other side of the lens
Nature - Real and inverted
(b)
PAGE 10 {31/1/1}
(c) (i)
f1 = 30 cm = 0.3 m, f 2 = -15cm = -0.15 m
P=f
+1 −1
P1= 0.3 D ; P2= 0.15 D
Equivalent power, P = P1+P2
P = - 3.33D
Equivalent focal length, f =
P
−1
f = 3.33 = - 0.3 m = - 30 cm
OR
(c) (ii)
• Combination Lens will behave like convex lens
• f 1 = - 2 m, f 2 = 1.5 m
P=f
−1 +1
P1= 2 D , P2= 1.5 D
P = P1+P2
P=6
f = + 6m
The focal length of combination is positive.
/
Alternate answer
• Combination Lens will behave like convex lens.
• Convex lens - Less ‘f’, More ‘P1’
Concave lens - More ‘f’, Less ‘P2’
Combined Power = P1+P2, which will be positive.