Question

The given figure shows image formation by a lens. Analyse the figure and answer the following questions : 


What is the type of lens used for image formation in the given ray diagram ? 
If the real image is formed at a distance of \( 30 \text{ cm} \) from the lens and the size of image is twice the size of the object, then where was the object placed ? 
 

Hint:

Always use sign convention: Real images in lenses have positive \( v \), and object distance \( u \) is always negative.

Answer 1

Analysis of the Given Ray Diagram:

From the figure: – The image formed is real and inverted.
– The rays actually meet on the other side of the lens.
– This type of image is produced only by a convex (converging) lens.

Answer 1: Type of Lens Used
\[ \boxed{\text{Convex lens}} \] A concave lens always forms virtual and erect images, so the given diagram must represent a convex lens.

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Second Part: Finding Object Position

Given: Image distance \( v = 30 \, \text{cm} \)
Image size is twice the size of object. This means magnification: \[ m = 2 \] Since the image is real and inverted: \[ m = -2 \] We know: \[ m = \frac{v}{u} \] Substitute values: \[ -2 = \frac{30}{u} \] \[ u = \frac{30}{-2} \] \[ u = -15 \, \text{cm} \]

Final Answer: \[ \boxed{\text{Object was placed } 15 \text{ cm in front of the lens}} \] (Negative sign indicates object is on the left side of the lens.)

Conclusion:
– The lens used is a convex lens.
– If the real image is formed at 30 cm and is twice the size of the object, then the object was placed 15 cm from the lens (between F and 2F).