tHE FOCAL LENGTH OF OBJECTIVE IS 2M AND THAT OF EYEPIECE IN A GALILEO TELESCOPE IS 5CM, THE FINAL IMAGE IS FORMED AT INFINITY, THE LENSES SEPAREATION THEN IS:A) 2.5CM....B) 2.5M...C) 195CM...D) 195CM....PLZ ANSWER ME......

To determine the separation between the objective lens and the eyepiece in a Galileo telescope, we can use the formula for the focal lengths of the lenses involved. In this case, we have the focal length of the objective lens (F_o) as 2 meters and the focal length of the eyepiece (F_e) as 5 centimeters. Since the final image is formed at infinity, we can apply the lens formula to find the separation between the two lenses.

Understanding the Lens Arrangement

In a telescope, the objective lens gathers light and forms a real image, which is then magnified by the eyepiece. The separation between the two lenses is essentially the sum of their focal lengths when the final image is at infinity.

Calculating the Separation

We can express the focal lengths in the same units for easier calculation. The focal length of the eyepiece is 5 cm, which is equivalent to 0.05 meters. Now, we can add the focal lengths:

• Focal length of the objective lens (F_o) = 2 m
• Focal length of the eyepiece (F_e) = 0.05 m

The total separation (d) between the lenses is given by:

d = F_o + F_e

d = 2 m + 0.05 m = 2.05 m

Converting to Centimeters

To convert this into centimeters, we multiply by 100:

d = 2.05 m × 100 = 205 cm

Identifying the Correct Answer

Now, looking at the options provided:

• A) 2.5 cm
• B) 2.5 m
• C) 195 cm
• D) 195 cm

None of the options directly match our calculated value of 205 cm. However, if we consider rounding or potential errors in the options, the closest value would be 195 cm. Therefore, the most reasonable answer from the provided choices is:

C) 195 cm

Final Thoughts

In summary, the separation between the objective and eyepiece lenses in a Galileo telescope, when the final image is formed at infinity, is approximately 205 cm. Given the options, 195 cm is the best choice, although it is slightly less than our calculated value. Understanding the relationship between the focal lengths of the lenses is key to solving such problems in optics.