Answer:
d)60cm
Step-by-step explanation:
When an object is placed in front of a plane mirror, its image is formed behind the mirror at the same distance as the object is in front of the mirror. This means that the image distance (d_i) is equal to the object distance (d_o):
d_i = d_o
Initially, the object is placed 30 cm in front of the mirror, so the image distance is also 30 cm.
When the mirror is moved a distance of 6 cm towards the object, the new object distance becomes:
d_o' = d_o - 6 cm = 30 cm - 6 cm = 24 cm
Using the mirror formula, we can find the image distance for the new object distance:
1/d_o' + 1/d_i' = 1/f
where f is the focal length of the mirror, which is infinity for a plane mirror. Therefore, we can simplify the equation to:
1/d_o' + 1/d_i' = 0
Solving for d_i', we get:
1/d_i' = -1/d_o'
d_i' = - d_o'
Substituting the given values, we get:
d_i' = -24 cm
Since the image distance is negative, this means that the image is formed behind the mirror and is virtual (i.e., it cannot be projected onto a screen).
The distance between the object and its image is the difference between their positions:
distance = d_i' - d_o = (-24 cm) - (30 cm) = -54 cm
Since the image is virtual, we can take the absolute value of the distance to get the magnitude:
|distance| = |-54 cm| = 54 cm
Therefore, the distance between the object and its image is 54 cm. The answer is (d) 60 cm, which is the closest option to 54 cm.