Introduction:
In this scenario, we have a point source located at a distance of 35 cm on the optical axis from a spherical concave mirror. The concave mirror has a focal length of 25 cm. We need to determine the distance along the optical axis from the concave mirror where a plane mirror should be placed so that the image it forms coincides with the point source.

Step 1: Understanding the properties of a concave mirror:
Before we proceed, let's first understand the properties of a concave mirror. A concave mirror is a spherical mirror with a reflecting surface that curves inward. It can form both real and virtual images depending on the position of the object relative to the focal point.

Step 2: Determining the position of the image formed by the concave mirror:
To find the distance where the plane mirror should be placed, we first need to determine the position of the image formed by the concave mirror.

Step 2.1: Using the mirror formula:
The mirror formula is given by:

1/f = 1/v - 1/u

Where:
f = focal length of the concave mirror
v = image distance from the mirror
u = object distance from the mirror (negative for objects on the same side as the incident light)

In this case, the focal length (f) is 25 cm and the object distance (u) is -35 cm (as it is on the same side as the incident light). We need to solve the equation to find the image distance (v).

1/25 = 1/v - 1/-35

Simplifying the equation, we get:

1/v = 1/25 + 1/35

1/v = (35 + 25)/(25 * 35)

1/v = 60/875

v = 875/60

v ≈ 14.58 cm

Step 2.2: Determining the position of the image:
Since the image distance (v) is positive, the image formed by the concave mirror is real and located 14.58 cm from the mirror on the opposite side of the object.

Step 3: Placing the plane mirror:
To make the image formed by the plane mirror coincide with the point source, the plane mirror should be placed at twice the distance of the image formed by the concave mirror.

Distance from the concave mirror to the plane mirror = 2 * v
Distance from the concave mirror to the plane mirror = 2 * 14.58 cm
Distance from the concave mirror to the plane mirror ≈ 29.16 cm

Conclusion:
To make the image formed by the plane mirror coincide with the point source, the plane mirror should be placed at a distance of approximately 29.16 cm along the optical axis from the concave mirror. This will ensure that the light rays from the point source reflect off the plane mirror and create an image that coincides with the source.