Two thin convex lenses L1 and L2,have focal lengths 4 cm and 10 cm, respectively. They are separated by a distance of x cm as shown in the figure. A point source S is placed on the principal axis at a distance 12 cm to the left of L1. If the image of S is formed at infinity, the value of x is:
Thus, the image distance \( v_1 = 6 \, \text{cm} \) (to the right of \( L_1 \)).
Step 2: Condition for Final Image at Infinity
For the final image to be at infinity, the image formed by \( L_1 \) must lie at the focal point of \( L_2 \). Therefore:
\[ x - v_1 = f_2 \]
\[ x - 6 = 10 \]
\[ x = 16 \, \text{cm} \]
Conclusion:
The required separation \( x \) between the lenses is 16 cm.
Answer: \(\boxed{B}\)
Was this answer helpful?
7
26
Hide Solution
Verified By Collegedunia
Approach Solution -2
Let $f_1$ be the focal length of lens L₁ and $f_2$ be the focal length of lens L₂.
Given $f_1 = 4$ cm and $f_2 = 10$ cm. Let $u_1$ be the object distance for L₁. $u_1 = -12$ cm (since it is to the left of L₁).
Let $v_1$ be the image distance for L₁. Using the lens formula for L₁: $\frac{1}{v_1} - \frac{1}{u_1} = \frac{1}{f_1}$ $\frac{1}{v_1} - \frac{1}{-12} = \frac{1}{4}$ $\frac{1}{v_1} = \frac{1}{4} - \frac{1}{12}$ $\frac{1}{v_1} = \frac{3-1}{12} = \frac{2}{12} = \frac{1}{6}$ $v_1 = 6$ cm.
The image formed by L₁ acts as an object for L₂. Let $u_2$ be the object distance for L₂.
The separation between the lenses is $x$ cm.
The image formed by L₁ is at a distance of 6 cm to the right of L₁. $u_2 = -(x-6)$ cm (negative as the object is to the right of L₂). The image is formed at infinity, so $v_2 = \infty$.
Using the lens formula for L₂: $\frac{1}{v_2} - \frac{1}{u_2} = \frac{1}{f_2}$ $\frac{1}{\infty} - \frac{1}{-(x-6)} = \frac{1}{10}$ $0 + \frac{1}{x-6} = \frac{1}{10}$ $x-6 = 10$ $x = 10+6$ $x = 16$ cm.
Final Answer: The final answer is $\boxed{B}$
Was this answer helpful?
0
0
Top Questions on Ray optics and optical instruments
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.
