Question

An object of height \( h \) is placed midway between \( f \) and \( 2f \) in front of a biconvex lens. A real inverted image is captured on a screen placed a little beyond \( 2f \) on the other side of the lens. If the whole arrangement is immersed in water without disturbing the object, lens and the screen positions, then the new image formed will be

• A. Magnified virtual erect image on the same side of the lens where the object is placed
• B. Magnified real inverted image on the same side of the lens where the object is placed
• C. Diminished real inverted image on the other side of the lens between \( f \) and \( 2f \)
• D. Magnified real inverted image on the other side of the lens beyond \( 2f \)

Hint:

When a convex lens is immersed in water, its relative refractive index decreases, so its power decreases and focal length increases.

Answer 1

The Correct Option is A

Step 1: Understand the initial condition.
The object is placed midway between \( f \) and \( 2f \) of a biconvex lens.
So the object lies between focus and twice the focal length.
For a convex lens, when the object is between \( f \) and \( 2f \), the image formed is real, inverted, magnified and beyond \( 2f \).

Step 2: Effect of immersing the lens in water.
The focal length of a lens depends on the refractive index of the lens relative to the surrounding medium.
Lens maker formula is:
\[ \frac{1}{f} = \left(\frac{\mu_l}{\mu_m}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right) \]

Step 3: Compare air and water medium.
Initially, the surrounding medium is air.
When the lens is immersed in water, the relative refractive index \( \frac{\mu_l}{\mu_m} \) decreases.
Therefore, the power of the lens decreases.

Step 4: Effect on focal length.
Since power decreases, focal length increases because:
\[ P = \frac{1}{f} \]
So, the new focal length of the biconvex lens becomes greater than the original focal length.

Step 5: Effect on object position.
The object position is not changed.
But due to increase in focal length, the object may now lie within the new focal length of the lens.
For a convex lens, when the object lies within the focal length, the image formed is virtual, erect and magnified.

Step 6: Identify the side of image formation.
A virtual image formed by a convex lens is produced on the same side of the lens as the object.
Therefore, the new image will be on the same side as the object.

Step 7: Conclusion.
Thus, after immersing the arrangement in water, the new image formed will be magnified, virtual and erect on the same side of the lens where the object is placed.
\[ \boxed{\text{Magnified virtual erect image on the same side of the lens where the object is placed}} \]