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INCONSISTENCY OF CONCEPT
OF FOCUS IN CONCAVE
MIRROR
CONSIDER AN INCIDENT RAY I1 - A
INCIDENT ON THE REFLECTING
SURFACE OF A CONCAVE MIRROR
PARALLEL TO THE PRINCIPAL AXIS
THE CENTRE OF CURVATURE AND
FOCUS ARE LOCATED ON THE
PRINCIPAL AXIS
CENTRE OF
CURVATURE
FOCUS
F
C
I1
A
NEWTON’S FIRST LAW
OF REFLECTION STATES THAT THE
ANGLE OF INCIDENCE EQUALS THE
ANGLE OF REFLECTION AT THE
POINT OF INCIDENCE WHEN
MEASURED FROM THE NORMAL
HENCE WE DRAW A TANGENT AT
POINT A ON THE CONCAVE MIRROR
CENTRE OF
CURVATURE
FOCUS
C F
I1
TANGENT
A
FROM NEWTON’S FIRST LAW WE
HAVE ANGLE I1-A-C = ANGLE C-A-F
ALSO ANGLE I1-A-C = ANGLE A-C-F
SINCE
THEY ARE ALTERNATE ANGLES
IN TRIANGLE ACF SIDE AF = SIDE FC
SINCE TRIANGLE ACF IS AN
ISOCELES TRIANGLE
CENTRE OF
CURVATURE
FOCUS
C F
TANGENT
A
I1
1
1
1
NOW WE DRAW ANOTHER
INCIDENT RAY I2-B INCIDENT AT
THE CONCAVE MIRROR AT POINT B
AND THE RAY IS PARALLEL TO THE
PRINCIPAL AXIS CENTRE OF
CURVATURE
FOCUS
C F
I1
TANGENT
A
BI2
1
1
1
WE HAVE ALREADY DEDUCED FROM
THE INCIDENT RAY I1-A THAT
SIDE AC = SIDE FC.
SIMILARLY IN TRIANGLE CFB,
SIDE FB = SIDE FC CENTRE OF
CURVATURE
FOCUS
TANGENT
AI1
I2
C F
1
1
1
B
2
2
2
NOW AS DEDUCED EARLIER,
AF = FC AND
FC = FB
THEREFORE AF = FC = FB
OR
AF = FB
CENTRE OF
CURVATURE
FOCUS
TANGENT
AI1
I2
C F
1
1
1
B
2
2
2
WE HAVE ARBITRARILY DRAWN THE
INCIDENT RAYS I1-A AND I2-B
NOW A CONCAVE MIRROR IS A
PART OF A SPHERE WITH THE
PRINCIPAL AXIS AS A DIAMETER
AND POINT C AS ITS CENTRE OF
CURVATURE.
IF AF = FB, IT IMPLIES THAT THE FOCUS
WHERE ALL INCIDENT RAYS PARALLEL
TO THE PRINCIPAL AXIS CONVERGE IS
ANOTHER CENTRE TO THE SAME SPHERE OF
WHICH THE MIRROR IS A PART. THAT IS, IF
ANGLE 1 IS VERY LARGE SAY ALMOST 90 DEGREES AND
ANGLE 2 IS VERY SMALL SAY ALMOST 0 DEGREES, IT IS NOT POSSIBLE
FOR SIDE AF TO BE EQUAL TO SIDE FB
CENTRE OF
CURVATURE
FOCUS
TANGENT
AI1
I2
C F
1
1
1
B
2
2
2
THIS IS A CONTRADICTION TO THE CONCEPT
OF FOCUS IN A CONCAVE MIRROR

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INCONSISTENCY OF CONCEPT OF FOCUS WITH NEWTON'S LAW OF REFLECTION; PHYSICS; PHYSICAL SCIENCES

  • 1. INCONSISTENCY OF CONCEPT OF FOCUS IN CONCAVE MIRROR
  • 2. CONSIDER AN INCIDENT RAY I1 - A INCIDENT ON THE REFLECTING SURFACE OF A CONCAVE MIRROR PARALLEL TO THE PRINCIPAL AXIS THE CENTRE OF CURVATURE AND FOCUS ARE LOCATED ON THE PRINCIPAL AXIS CENTRE OF CURVATURE FOCUS F C I1 A
  • 3. NEWTON’S FIRST LAW OF REFLECTION STATES THAT THE ANGLE OF INCIDENCE EQUALS THE ANGLE OF REFLECTION AT THE POINT OF INCIDENCE WHEN MEASURED FROM THE NORMAL HENCE WE DRAW A TANGENT AT POINT A ON THE CONCAVE MIRROR CENTRE OF CURVATURE FOCUS C F I1 TANGENT A
  • 4. FROM NEWTON’S FIRST LAW WE HAVE ANGLE I1-A-C = ANGLE C-A-F ALSO ANGLE I1-A-C = ANGLE A-C-F SINCE THEY ARE ALTERNATE ANGLES IN TRIANGLE ACF SIDE AF = SIDE FC SINCE TRIANGLE ACF IS AN ISOCELES TRIANGLE CENTRE OF CURVATURE FOCUS C F TANGENT A I1 1 1 1
  • 5. NOW WE DRAW ANOTHER INCIDENT RAY I2-B INCIDENT AT THE CONCAVE MIRROR AT POINT B AND THE RAY IS PARALLEL TO THE PRINCIPAL AXIS CENTRE OF CURVATURE FOCUS C F I1 TANGENT A BI2 1 1 1
  • 6. WE HAVE ALREADY DEDUCED FROM THE INCIDENT RAY I1-A THAT SIDE AC = SIDE FC. SIMILARLY IN TRIANGLE CFB, SIDE FB = SIDE FC CENTRE OF CURVATURE FOCUS TANGENT AI1 I2 C F 1 1 1 B 2 2 2
  • 7. NOW AS DEDUCED EARLIER, AF = FC AND FC = FB THEREFORE AF = FC = FB OR AF = FB CENTRE OF CURVATURE FOCUS TANGENT AI1 I2 C F 1 1 1 B 2 2 2
  • 8. WE HAVE ARBITRARILY DRAWN THE INCIDENT RAYS I1-A AND I2-B NOW A CONCAVE MIRROR IS A PART OF A SPHERE WITH THE PRINCIPAL AXIS AS A DIAMETER AND POINT C AS ITS CENTRE OF CURVATURE. IF AF = FB, IT IMPLIES THAT THE FOCUS WHERE ALL INCIDENT RAYS PARALLEL TO THE PRINCIPAL AXIS CONVERGE IS ANOTHER CENTRE TO THE SAME SPHERE OF WHICH THE MIRROR IS A PART. THAT IS, IF ANGLE 1 IS VERY LARGE SAY ALMOST 90 DEGREES AND ANGLE 2 IS VERY SMALL SAY ALMOST 0 DEGREES, IT IS NOT POSSIBLE FOR SIDE AF TO BE EQUAL TO SIDE FB CENTRE OF CURVATURE FOCUS TANGENT AI1 I2 C F 1 1 1 B 2 2 2
  • 9. THIS IS A CONTRADICTION TO THE CONCEPT OF FOCUS IN A CONCAVE MIRROR