Question

Draw the ray diagram for the image formation by a lens which shows a magnification of +2.

Hint:

Magnification +2 means virtual, erect, enlarged image. Only convex lens can produce this when object is between F and O. Image is formed on same side, beyond 2F (virtual).

Answer 1

Step 1: Interpret the given magnification.
Magnification \( m = +2 \) means:

• The positive sign indicates that the image is virtual and erect (for a lens, positive magnification means virtual image on the same side as the object).
• The magnitude \( |m| = 2 \) means the image is twice the size of the object (enlarged).

Step 2: Determine which lens produces such an image.

• A convex lens can produce a virtual, erect, and enlarged image when the object is placed between the optical centre (O) and the focus (F).
• A concave lens always produces a virtual, erect, but diminished image (|m|<1), so it cannot give magnification 2.

Therefore, the lens must be a convex lens with the object placed between F and O.
Step 3: Ray diagram construction.

Step 4: Description of the ray diagram.

• The object (upright arrow) is placed between the optical centre (O) and the focus (F) on the left side of the convex lens.
• Ray 1: A ray parallel to the principal axis passes through the lens and appears to diverge from the focus on the same side as the object (virtual focus).
• Ray 2: A ray passing through the optical centre goes straight without deviation.
• The two rays diverge after refraction and do not actually meet. When extended backwards (dashed lines), they appear to meet at a point on the same side as the object.
• The image formed is virtual, erect, and enlarged (twice the size of object, i.e., magnification +2).
• The image is located on the same side as the object, beyond 2F.

Step 5: Verification of magnification.
In this position (object between F and O):

• Image distance>object distance (|v|>|u|)
• Image height>object height (enlarged)
• Image is virtual and erect \(\Rightarrow\) positive magnification
• For m = +2, the image distance is twice the object distance (approximately)

Step 6: Final answer.
The ray diagram shows a convex lens with object between F and O, forming a virtual, erect, and enlarged image (m = +2) on the same side as the object.}}