Lecture Notes: Understanding Concave Mirrors

Problem Statement

• Object Location: 12 cm in front of a concave mirror
• Focal Length: 8 cm
• Tasks:
  • Calculate the image position
  • Determine magnification
  • Interpret the nature of the image

Key Concepts

Mirror Equation

• Formula: ( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} )
  • ( f ): Focal Length
  • ( d_o ): Distance of the Object
  • ( d_i ): Distance of the Image
• Rearranged to find ( d_i ):
  • ( \frac{1}{d_i} = \frac{1}{f} - \frac{1}{d_o} )

Solution Steps

1. Substitute Values:
   • ( \frac{1}{d_i} = \frac{1}{8} - \frac{1}{12} )
   • Convert fractions to decimals: ( 0.125 - 0.08333 )
2. Calculate ( d_i ):
   • Reciprocal of the result gives ( d_i = 24 ) cm

Magnification

• Formula: ( M = \frac{-d_i}{d_o} )
  • Substituting Values: ( M = \frac{-24}{12} = -2 )
  • Interpretation: Image is magnified twice and inverted

Image Characteristics

• Image Distance (( d_i )):
  • Positive: Image formed in front of the mirror (Real Image)
• Magnification (( M )):
  • Negative: Image is inverted
  • Magnitude: Image is twice the size of the object

Conventions

• Image Distance (( d_i )):
  • Positive: Real Image (in front of mirror)
  • Negative: Virtual Image (behind mirror)
• Object Distance (( d_o )): Always positive
• Focal Length:
  • Positive: Concave Mirror
  • Negative: Convex Mirror

Example Problem

• Given:
  • Focal Length: 10 cm
  • Object Distance: 18 cm
  • Object Height: 9 cm
• Task:
  • Draw ray diagram
  • Calculate image distance and height

Conclusion

• Findings:
  • Image distance: 24 cm
  • Image is twice the size and inverted
• Tasks:
  • Use ray diagrams and mirror equations for further practice

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