9th SCIENCE and Mathematics NCERT SOLUTIONS

9TH SCIENCE NCERT SOLUTIONS
Chap 6 - TISSUES              

  IX Mathematics NCERT Solutions





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Derivation of Lens and mirror formula X Reflection and Refraction of light

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MIRROR FORMULA The relation between object distance(u), image distance(v) and the focal length (f) of the mirror is known as MIRROR FORMULA. Consider a concave mirror MM' (of small aperture). An object AB of height h is placed on the left of the mirror beyond its center of curvature so that the image formed is real, inverted and diminished in size(height = h'). Here : Object distance = PB = -u Image distance = PB'= -v Focal length = PF = -f Radius of curvature = PC = -R As shown in Figure, Δ ABP ∼ Δ A'B'P. ∴ A'B'/AB = PB'/PB ∴ A'B'/AB = (-v)/(-u) ∴ A'B'/AB = v/u.............(I) Similarly, as shown in the figure, Δ ABC ∼ Δ A'B'C. ∴ A'B'/AB = CB'/CB ∴ A'B'/AB = (PC-PB')/(PB-PC)........[as CB'=(PC-PB') and CB=(PB-PC)] ∴ A'B'/AB = [-R - (-v)]/[-u - (-R)] ∴ A'B'/AB = (-R + v)/(-u + R)........(II) By (I) & (II), v/u = (-R + v)/(-u + R) ∴ -...
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