#mirror formula

Combination of Lenses and Lens Systems

A convex mirror has a radius of curvature of \( 50 \, \text{cm} \). An object is placed \( 25 \, \text{cm} \) from it. W

**Lens combination** effective focal length calculation uses reciprocal sum, for f₁=10 cm, f₂=20 cm in contact, 1/F=1/10+1/20=3/20, F=6.67 cm, P=15 D, stronger converging than either alone, illustrating power addition. Focal length: f = (R/2) = (50/2) = 25 cm (positive for convex). Object distance: u = -25 cm . Mirror equation: (1/v) + (1/u) = (1/f) . (1/v) + (1/-25) = (1/25) ⇒ (1/v) = (1/25) + (1/25) = (2/25) . v = (25/2) = 12.5 cm (virtual image). Substituting values gives 12.5 cm, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v - 1/u (lens) or 1/f

Ref: NCERT > Physics Book > Ray Optics > Combination of Lenses and Lens Systems

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Refraction at Spherical Surfaces and Lens Maker's Formula

An object is placed \( 18 \, \text{cm} \) from a convex mirror of focal length \( 12 \, \text{cm} \). What is the image

**Refraction at spherical surface** formula n₁/u + n₂/v = (n₂-n₁)/R governs single surface, extension to two surfaces yields lens maker. Double convex with equal |R| has f = R/[2(n-1)], for R=12 cm, n=1.5, f=12 cm, illustrating dependence on curvature and index. Focal length: f = 12 cm , u = -18 cm . Mirror equation: (1/v) + (1/-18) = (1/12) ⇒ (1/v) = (1/12) + (1/18) = (3 + 2/36) = (5/36) . v = (36/5) = 7.2 cm (virtual image). Substituting values gives 7.2 cm, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v - 1/u (lens) or 1/f =

Ref: NCERT > Physics Book > Ray Optics > Refraction at Spherical Surfaces and Lens Maker's Formula

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Refraction Through Prism and Minimum Deviation

An object is placed \( 10 \, \text{cm} \) from a convex mirror of radius of curvature \( 30 \, \text{cm} \). What is the

**Prism minimum deviation** δ_m satisfies n = sin[(A+δ_m)/2]/sin(A/2), A prism angle (degrees), n refractive index, δ_m minimum deviation. For A=60°, n=1.45, sin[(60+δ_m)/2]=1.45×sin30°=0.725, (60+δ_m)/2=46.5°, 60+δ_m=93°, δ_m=33°, illustrating n increase raises δ_m. f = (R/2) = (30/2) = 15 cm . u = -10 cm . (1/v) + (1/-10) = (1/15) ⇒ (1/v) = (1/15) + (1/10) = (2 + 3/30) = (5/30) = (1/6) . v = 6 cm (virtual image). Substituting values gives 6 cm, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v - 1/u (lens) or 1/f = 1/v + 1/u (mirror), confirming sign

Ref: NCERT > Physics Book > Ray Optics > Refraction Through Prism and Minimum Deviation

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Optical Instruments - Simple and Compound Microscope

A concave mirror has a radius of curvature of \( 40 \, \text{cm} \). An object of height \( 2 \, \text{cm} \) is placed

**Compound microscope** M = m_o × M_e, objective magnification m_o = v_o/u_o ≈ L/f_o, L tube length, eyepiece M_e = 1+D/f_e (image at D) or D/f_e (infinity). Objective forms real inverted magnified image at focal plane of eyepiece, eyepiece acts as simple microscope magnifying it. Focal length: f = (R/2) = (-40/2) = -20 cm (negative for concave mirror). Object distance: u = -30 cm . Using mirror equation: (1/v) + (1/u) = (1/f) . (1/v) + (1/-30) = (1/-20) ⇒ (1/v) = (1/-20) + (1/30) = (-3 + 2/60) = (-1/60) . v = -60 cm (real image). Magnification: m = -(v/u) = -(-60/-30)

Ref: NCERT > Physics Book > Ray Optics > Optical Instruments - Simple and Compound Microscope

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Reflection by Spherical Mirrors and Mirror Formula

A convex mirror of radius of curvature \( 36 \, \text{cm} \) has an object placed \( 27 \, \text{cm} \) from it. What is

**Concave mirror image formation** depends on object position: beyond C real inverted diminished between F and C, at C real inverted same size at C, between C and F real inverted magnified beyond C, at F image at infinity, within F virtual erect magnified behind mirror. Focal length: f = (R/2) = (36/2) = 18 cm (convex mirror). Object distance: u = -27 cm . Mirror equation: (1/v) + (1/u) = (1/f) . (1/v) + (1/-27) = (1/18) ⇒ (1/v) = (1/18) + (1/27) = (3 + 2/54) = (5/54) . v = (54/5) = 10.8 cm (virtual image). Substituting values gives 9 cm, which

Ref: NCERT > Physics Book > Ray Optics > Reflection by Spherical Mirrors and Mirror Formula

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Reflection by Spherical Mirrors and Mirror Formula

A concave mirror of focal length \( 15 \, \text{cm} \) forms an image at \( 30 \, \text{cm} \) from the mirror. What is

**Mirror formula** 1/f = 1/v + 1/u governs spherical mirrors, f = R/2, R radius of curvature (m), u object distance (m), v image distance (m), sign convention: distances in front of mirror negative for real is convention but magnitude used, magnification m = -v/u, concave forms real inverted when object beyond F, virtual erect within F. Focal length: f = -15 cm (concave mirror). Image distance: v = -30 cm (real image, same side as object). Mirror equation: (1/v) + (1/u) = (1/f) . (1/-30) + (1/u) = (1/-15) ⇒ (1/u) = (1/-15) + (1/30) = (-2 + 1/30) = (-1/30) . u =

Ref: NCERT > Physics Book > Ray Optics > Reflection by Spherical Mirrors and Mirror Formula

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