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An object is placed 30cm in front of plane mirror. If the mirror is moved a distance of 6cm towards the object, find the distance between the object and it's image.

a)24cm b)36cm c)48cm d)60cm​

User Elease
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1 Answer

4 votes

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.

User Bagus Tesa
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