Two plane mirrors are placed parallel to each other and 40cmapart. An object is placed 10cmfrom one mirror. Determine the (a) smallest, (b) second smallest, (c) third smallest (occurs twice), and (d) fourth smallest distance between the object and image of the object.

Short Answer

Expert verified
  1. The smallest distance between the object and the image of the object is 20cm.
  2. The second smallest distance between the object and the image of the object is60cm.
  3. The third smallest (occurs twice) distance between the object and the image of the object is80cm.
  4. The fourth smallest distance between the object and the image of the object is 100cm.

Step by step solution

01

The given data:

  • Distance between two parallel plane mirrors is40cm.
  • Distance between object and first mirror is 10cm.
02

Understanding the concept of image formation in theplane mirror

As two plane mirrors are placed parallel to each other separated by a distance of 40cm, they will form images as shown in the below diagram. Each mirror produces a first image of the object. Then, each mirror produces a second image with the object being the first image in the opposite mirror. Then each mirror produces a third image with the object being the second image in the opposite mirror, and so on. Therefore, the mirrors will produce five images. Here, you find the smallest distance, second smallest distance, third smallest distance, and fourth smallest distance between the object and an image of the object.

03

(a) Calculation of the smallest distance between the object and the image:

To know the smallest distance, yourefer the above figure. In the closest mirrorM1, the “first” imageI1is 10cm behindrole="math" localid="1663022915939" M1and thus,20cm from the object O. This is the smallest distance between the object and an image of the object.

Hence, the smallest distance is 20cm.

04

(b) Calculation of the second smallest distance between the object and the image:

To know the second smallest distance, refer the above figure. There are images from both OandI1in the more distant mirror,M2an imageI2located at 30cmbehindM2. Since Ois 30cm in front of it,I2is 60cm from O. This is the second smallest distance between the object and an image of the object.

Hence, the second smallest distance is 60cm.

05

(c) Calculation of the third smallest distance between the object and the image:

To know the third smallest distance, refer the above figure. There is also an image I3that is 50cmbehind M2 (since I1 is 50cm in front of it). Thus, I3is 80cmfrom O. In addition, you have another image I4that is 70cm behind role="math" localid="1663023685109" M1 (since I2 is 70cm in front of it). The distance from I4 to O for is 80cm.

Hence, the third smallest distance is 80cm.

06

(d) Calculation of the fourth smallest distance between the object and the image

To know the fourth smallest distance, yourefer the above figure. Returning to the closer mirrorM1, there is an imageI5that is 90cm behind the mirror (sincerole="math" localid="1663023840894" I3is 90cm in front of it). The distance (measured from O) is found to be 100cmforI5.

Hence, the fourth smallest distance is 100cm.

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