1. Given Data

• Distance between mirrors (d): 20 mm
• Radius of curvature of Large Mirror (R₁): 220 mm (Concave)
• Radius of curvature of Small Mirror (R₂): 140 mm (Convex)
• Object Position: At Infinity

2. Calculating Focal Lengths

The focal length (f) is half of the radius of curvature (R/2).

Primary Mirror (Concave):

f₁ = R₁ / 2 = 220 / 2 = 110 mm

(Sign convention: Concave focal length is negative, f₁ = -110 mm. The image forms in front of it.)

Secondary Mirror (Convex):

f₂ = R₂ / 2 = 140 / 2 = 70 mm

(Sign convention: Convex focal length is positive, f₂ = +70 mm.)

3. Image formed by Primary Mirror

Since the object is at infinity, the primary mirror forms the image at its focus.

Position of first image (I₁) from primary mirror = 110 mm.

This image I₁ acts as a Virtual Object for the secondary mirror.

4. Image formed by Secondary Mirror

Step A: Find Object Distance (u)

The primary image is formed 110 mm from the primary mirror. The secondary mirror is placed 20 mm in front of the primary mirror.

Distance of virtual object from secondary mirror (u):

u = Distance of I₁ - Separation (d)

u = 110 - 20

u = +90 mm (Positive because it is behind the secondary mirror)

Step B: Apply Mirror Formula

1/v + 1/u = 1/f₂

Substituting values:

• 1/v + 1/90 = 1/70
• 1/v = 1/70 - 1/90
• 1/v = (9 - 7) / 630
• 1/v = 2 / 630
• 1/v = 1 / 315
• v = 315 mm

Conclusion: The final image is formed at a distance of 315 mm from the secondary mirror (away from the primary mirror).