A question on geometric optics

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SUMMARY

This discussion centers on the optical properties of a concave mirror with a 5 cm radius of curvature and a 4 cm radius for its blackened circular ring. When a beam of light parallel to the principal axis strikes the mirror, it reflects off the non-blackened edge. The distance from the center of curvature to the focus point is determined by the mirror's geometry and the angle of incidence. The blackened area does not affect the focal point but may alter the intensity of the reflected light due to reduced surface area for reflection.

PREREQUISITES
  • Understanding of concave mirrors and their focal properties
  • Knowledge of geometric optics principles, including reflection and refraction
  • Familiarity with the concept of radius of curvature in optics
  • Basic skills in solving optical path length equations
NEXT STEPS
  • Explore the principles of ray tracing in concave mirrors
  • Study the effects of surface coatings on mirror reflectivity
  • Learn about the mathematical derivation of focal points in concave mirrors
  • Investigate the relationship between angle of incidence and reflection in optics
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This discussion is beneficial for physics students, optical engineers, and anyone interested in the principles of geometric optics and mirror behavior.

roborahull
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a concave mirror of 5cm radius of curvature whose circular ring has a radius of 4cm is blackened except for a narrow strip round the edge. A beam of light parallel to the principal axis falls on the mirror. Find the distance between the centre of curvature of mirror and the point at which light is focused.
 
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Greetings robarahull. Welcome to the forum.

To get help with homework questions you need to follow the rules. You need to fill in the template for asking questions. And you need to show that you have done some of the work trying to solve your homework yourself.

Because you are new I will give you a tiny bit of help anyway. What angle will the light make with the surface of the mirror at the non-black radius? And so where will it reflect? So where will it be focussed?
 
roborahull said:
a concave mirror of 5cm radius of curvature whose circular ring has a radius of 4cm is blackened except for a narrow strip round the edge. A beam of light parallel to the principal axis falls on the mirror. Find the distance between the centre of curvature of mirror and the point at which light is focused.

In the paraxial case, what difference does it make for a mirror to have its centre blackened? Will the intensity of the reflected light change? Will the focus point change (hint: optical path length)?
 

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