A thin rod of length 6 cm lies along the principal axis of the concave mirror of focal length 15 cm in such a way that the end closer to the pole is 30 cm away from it.  Then the length of the image isSelect an answerA4.28 cmB1.75 cmC3.75 cmD4.5 cm

To solve this problem, we need to use the mirror formula and magnification formula.

The mirror formula is 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.

The magnification formula is m = -v/u, where m is the magnification, v is the image distance, and u is the object distance.

Step 1: Find the image distance for both ends of the rod.

For the end closer to the pole (u = -30 cm), we can use the mirror formula to find v:

1/f = 1/v + 1/u 1/-15 = 1/v + 1/-30 Solving for v, we get v = -10 cm.

For the end farther from the pole (u = -36 cm), we can again use the mirror formula to find v:

1/f = 1/v + 1/u 1/-15 = 1/v + 1/-36 Solving for v, we get v = -12 cm.

Step 2: Find the length of the image.

The length of the image is the difference in the image distances, which is |-12 - (-10)| = 2 cm.

However, the image is inverted, so the actual length of the image is -2 cm.

Step 3: Find the magnification.

The magnification is the ratio of the image length to the object length, which is -2/6 = -0.33.

Step 4: Find the actual length of the image.

The actual length of the image is the magnification times the object length, which is -0.33 * 6 = -2 cm.

However, since the image is inverted, the actual length of the image is 2 cm.

So, none of the given options is correct. The length of the image should be 2 cm.

To solve this problem, we need to use the mirror formula and magnification formula.

The mirror formula is 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.

The magnification formula is m = -v/u, where m is the magnification, v is the image distance, and u is the object distance.

Step 1: Find the image distance for both ends of the rod.

For the end closer to the pole (u = -30 cm), we can substitute the values into the mirror formula:

1/f = 1/v + 1/u 1/-15 = 1/v + 1/-30 Solving for v, we get v = -10 cm.

For the end farther from the pole (u = -36 cm), we substitute the values into the mirror formula:

1/f = 1/v + 1/u 1/-15 = 1/v + 1/-36 Solving for v, we get v = -18 cm.

Step 2: Find the length of the image.

The length of the image is the difference in the image distances, which is |-18 - (-10)| = 8 cm.

Step 3: Find the magnification.

The magnification is the ratio of the image length to the object length, which is 8/6 = 1.33.

Step 4: Find the actual length of the image.

The actual length of the image is the magnification times the object length, which is 1.33 * 6 = 7.98 cm.

So, none of the given options are correct. The length of the image should be approximately 7.98 cm.