An object moving towards mirror as shown in the figure.A. the speed o…

The correct answer is Option (4) → B, C, E only

A plane mirror forms the image as far behind the mirror as the object is in front of it. Take the direction from the object towards the mirror as positive. If the mirror is at \( x_m \) and the object at \( x_o \), the image is at \( x_i = 2x_m - x_o \), so for velocities along the normal

    \( \displaystyle v_i = 2v_m - v_o, \qquad v_o = +2\,\mathrm{m\,s^{-1}} \)

(A) the speed of image will be 2 m/s irrespective of the speed of mirror. — Incorrect. The image velocity contains \( 2v_m \), so it depends on the motion of the mirror, as statements C and E show.

(B) the speed of image will be 2 m/s when speed of mirror is zero. — Correct. With \( v_m = 0 \):

    \( \displaystyle v_i = 0 - 2 = -2\,\mathrm{m\,s^{-1}} \;\Rightarrow\; \text{speed} = 2\,\mathrm{m\,s^{-1}} \)

(C) the speed of image will be 6 m/s when mirror is moving towards object with 2 m/s. — Correct. The mirror moves towards the object, so \( v_m = -2\,\mathrm{m\,s^{-1}} \):

    \( \displaystyle v_i = 2(-2) - 2 = -6\,\mathrm{m\,s^{-1}} \;\Rightarrow\; \text{speed} = 6\,\mathrm{m\,s^{-1}} \)

(D) the speed of image will be 6 m/s, where mirror is moving away from object with 2 m/s. — Incorrect. When the mirror moves away, \( v_m = +2\,\mathrm{m\,s^{-1}} \), and the image speed is 2 m/s, not 6 m/s (see E).

(E) the speed of image will be 2 m/s, where mirror is moving away from object with 2 m/s. — Correct. With \( v_m = +2\,\mathrm{m\,s^{-1}} \):

    \( \displaystyle v_i = 2(2) - 2 = +2\,\mathrm{m\,s^{-1}} \;\Rightarrow\; \text{speed} = 2\,\mathrm{m\,s^{-1}} \)