Question

An object is placed at 30 cm from a convex lens of focal length 20 cm. If the object is moved towards the lens by 5 cm, then the image is shifted by}

• A. 1 cm
• B. 40 cm
• C. 4 cm
• D. 10 cm
• E. 12 cm

Hint:

When the object is moved closer to a convex lens but still outside the focal length, the image can move much farther away. Always calculate both image positions separately.

Answer 1

The Correct Option is B

Use the lens formula: \[ \frac{1}{f}=\frac{1}{v}-\frac{1}{u} \] For the first position: \[ f=20\text{ cm},\qquad u=-30\text{ cm} \] So, \[ \frac{1}{20}=\frac{1}{v}-\left(-\frac{1}{30}\right) \] \[ \frac{1}{20}=\frac{1}{v}+\frac{1}{30} \] \[ \frac{1}{v}=\frac{1}{20}-\frac{1}{30}=\frac{1}{60} \] \[ v=60\text{ cm} \] Now the object is moved 5 cm towards the lens, so new object distance is: \[ u'=-25\text{ cm} \] Again using lens formula: \[ \frac{1}{20}=\frac{1}{v'}-\left(-\frac{1}{25}\right) \] \[ \frac{1}{20}=\frac{1}{v'}+\frac{1}{25} \] \[ \frac{1}{v'}=\frac{1}{20}-\frac{1}{25}=\frac{1}{100} \] \[ v'=100\text{ cm} \] Therefore, image shift is: \[ 100-60=40\text{ cm} \]
Hence, the correct answer is: \[ \boxed{(B)\ 40\text{ cm}} \]