Question

In an experiment to determine the focal length $\left(f\right)$ of a concave mirror by the $u-v$ method, a student places the object pin $A$ on the principal axis at a distance $x$ from the pole $P$. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with $PA$. When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then,

• A. $f<x<2f$
• B. $x=2f$
• C. $x<f$
• D. $x>2f$

Answer 1

The correct option is A $f<x<2f$


Since the image appears to the right of the object when the student shift eye towards the left, the image is nearer to the student, hence the image distance $"v"$ is greater than the object distance ${}^{\prime }{u}^{\prime }.$
This is possible only if the object is placed between $f$ and $2f.$

Also, the object and image move in opposite directions, the position of object should be in between $f$ and $2f$.

So, $f<x<2f.$

Hence, option (b) is the correct answer.