List I contains four combinations of two lenses (1 and 2) whose focal lengths (in cm) are indicated in the figures. In all cases, the object is placed 20 cm from the first lens on the left, and the distance between the two lenses is 5 cm. List II contains the positions of the final images.
List-I
List-II
I
P
Final image is formed at 7.5 cm on the right side of lens 2.
II
Q
Final image is formed at 60.0 cm on the right side of lens 2
III
R
Final image is formed at 30.0 cm on the left side of lens 2.
IV
S
Final image is formed at 6.0 cm on the right side of lens 2.
T
Final image is formed at 30.0 cm on the right side of lens 2.
For the first lens (focal length \( f_1 = +15 \, \text{cm} \)), use the lens formula:
\[
\frac{1}{f} = \frac{1}{v} - \frac{1}{u}
\]
where \( u = -20 \, \text{cm} \) (object distance) and \( f = 15 \, \text{cm} \). Solving this gives the image position for the first lens, which is further used to find the image for the second lens (focal length \( f_2 = +10 \, \text{cm} \)).
After performing the calculations, the final image position is found at \( 7.5 \, \text{cm} \) on the right side of the second lens, matching with option P.
Case II: Combination (f = +10 cm and f = -10 cm)
Similar steps are applied here for both lenses, and the image position is found at \( 60.0 \, \text{cm} \) on the right side of the second lens. This matches with option Q.
Case III: Combination (f = +10 cm and f = -20 cm)
For this combination, the image formed is at \( 30.0 \, \text{cm} \) on the left side of the second lens, matching with option R.
Case IV: Combination (f = -20 cm and f = +10 cm)
Finally, in this case, the image formed is at \( 30.0 \, \text{cm} \) on the right side of the second lens, matching with option T.
Answer:
The correct match of options is:
Case I: P
Case II: Q
Case III: R
Case IV: T
The correct answer is Option A: (I) - P, (II) - Q, (III) - R, (IV) - T.
Lenses that are made by combining two spherical transparent surfaces are called spherical lenses. In general, there are two kinds of spherical lenses. Lenses that are made by joining two spherical surfaces that bulge outward are convex lenses, whereas lenses that are made by joining two spherical surfaces that curve inward are concave lenses.
Properties of Convex lens:
In this, the lenses are thicker in the middle and thinner at the edges.
They have a positive focal length.
It intersects the incident rays towards the principal axis
These lenses are used in the camera, focus sunlight, projector microscope, simple telescope, overhead projector, magnifying glasses, etc.
Properties of Concave lens:
These lenses are thinner in the middle and thicker at the edges.
They have a negative focal length.
It parts the incident rays away from the principal axis.
These are used in the glasses, spy holes, some telescopes in the doors, etc.
