A reflecting telescope has a radius of curvature of 3m for its objective mirror and a radius of curvature of -1.5 for its eyepiece mirror. If the distance between the two mirrors is 0.90 m, how far in front of the eyepiece should you place the electronic sensor to record the image of a star?

Question

A reflecting telescope has a radius of curvature of 3m for its objective mirror and a radius of curvature of -1.5 for its eyepiece mirror. If the distance between the two mirrors is 0.90 m, how far in front of the eyepiece should you place the electronic sensor to record the image of a star?

Answer 1

To find the distance at which the electronic sensor should be placed in front of the eyepiece to record the image of a star in a reflecting telescope, we can use the mirror formula.

The mirror formula is given by:

1/f = 1/v - 1/u

Where:
f is the focal length of the mirror,
v is the image distance,
u is the object distance.

In this case, we can assume the distance between the two mirrors as the object distance for the eyepiece mirror since the objective mirror focuses the light rays onto the eyepiece mirror.

Let's calculate the focal length of the objective mirror first.

The formula for the focal length of a mirror is given by:

f = R/2

Where:
R is the radius of curvature of the mirror.

For the objective mirror:
f1 = R1/2 = 3/2 = 1.5 m

Now, let's calculate the focal length of the eyepiece mirror.

For the eyepiece mirror:
f2 = R2/2 = -1.5/2 = -0.75 m

Next, we need to find the image distance (v) for the eyepiece mirror.

Using the mirror formula for the eyepiece mirror:

1/f2 = 1/v - 1/u

Since the distance between the two mirrors is 0.90 m and the object distance (u) for the eyepiece mirror is equal to this distance:

1/-0.75 = 1/v - 1/0.90

Simplifying the equation:

-1.33 = 1/v - 1.11

Rearranging the equation:

1/v = -1.33 + 1.11
1/v = -0.22

Taking the reciprocal of both sides:

v = -1/0.22
v = -4.55 m

The negative sign indicates that the image formed by the eyepiece mirror is virtual and upright.

Finally, we need to calculate the distance at which the electronic sensor should be placed in front of the eyepiece mirror. This distance is equal to the image distance (v) plus the distance between the two mirrors:

Distance = v + object distance between the mirrors
Distance = -4.55 + 0.90
Distance = -3.65 m

Therefore, the electronic sensor should be placed approximately 3.65 meters in front of the eyepiece mirror to record the image of a star.

A reflecting telescope has a radius of curvature of 3m for its objective mirror and a radius of curvature of -1.5 for its eyepiece mirror. If the distance between the two mirrors is 0.90 m, how far in front of the eyepiece should you place the electronic sensor to record the image of a star?

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To find the distance at which the electronic sensor should be placed in front of the eyepiece to record the image of a star in a reflecting telescope, we can use the mirror formula.