#virtual image

Refraction at Spherical Surfaces and Lens Maker's Formula

Why is the image formed by a plane mirror always virtual?

**Lens maker's formula** 1/f = (n-1)(1/R₁ - 1/R₂), n refractive index, R₁,R₂ radii of curvature (m), sign convention R positive if surface convex towards incident light. For double convex R₁=12 cm, R₂=-12 cm, n=1.5, 1/f=(0.5)(1/12 -1/(-12))=(0.5)(2/12)=1/12, f=12 cm, converging. In a plane mirror, the reflected rays do not actually converge but appear to diverge from a point behind the mirror when traced backward. This apparent origin of rays behind the mirror results in a virtual image that cannot be projected onto a screen. Substituting values gives Due to apparent divergence from behind the mirror, which matches expected image position and magnification from mirror/lens formula 1/f

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Refraction at Spherical Surfaces and Lens Maker's Formula

Why does a convex mirror never produce a real image regardless of the object’s position?

**Lens maker's formula** 1/f = (n-1)(1/R₁ - 1/R₂), n refractive index, R₁,R₂ radii of curvature (m), sign convention R positive if surface convex towards incident light. For double convex R₁=12 cm, R₂=-12 cm, n=1.5, 1/f=(0.5)(1/12 -1/(-12))=(0.5)(2/12)=1/12, f=12 cm, converging. A convex mirror reflects light such that the rays diverge after reflection. These diverging rays appear to originate from a point behind the mirror, forming a virtual image. Since the rays do not actually converge, a real image (which requires convergence) cannot be formed. Substituting values gives Because reflected rays diverge, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v - 1/u

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

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Refraction at Spherical Surfaces and Lens Maker's Formula

In a concave lens, why is the image always formed on the same side as the object?

**Spherical refracting surface** power P = (n₂-n₁)/R, lens power sum of two surfaces. Lens maker derivation combines two refractions, sign of R₂ negative for second surface convex opposite direction, yielding 1/f positive for convex lens. A concave lens diverges light rays, making them appear to originate from a point on the same side as the object when traced backward. This results in a virtual image that cannot be projected on a screen, always forming on the object’s side regardless of its position. Substituting values gives Because rays diverge and appear to come from the same side, which matches expected image position and magnification from mirror/lens

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

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Total Internal Reflection and Critical Angle

In a concave mirror, under what condition is the image formed virtual and magnified?

**TIR application** requires n₁>n₂ and θ₁>C. Critical angle formula derived from Snell's law with θ₂=90°, n₁ sinC = n₂ sin90° = n₂, so sinC = n₂/n₁. For glass-air sinC=1/1.52, C≈41°, for water-air 48.6°, determining cutoff for transmission. For a concave mirror, a virtual and magnified image is formed when the object is placed between the focal point (F) and the pole (P). Here, the reflected rays diverge, and their backward extensions converge behind the mirror, producing a virtual, erect, and magnified image. Substituting values gives Object between focal point and pole, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v -

Ref: NCERT > Physics Book > Ray Optics > Total Internal Reflection and Critical Angle

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Refraction at Plane Surfaces and Snell's Law

In a convex lens, why does the image transition from virtual to real as the object moves from inside to outside the foca

**Refractive index** n = c/v, water 1.33 means light 1.33 times slower than vacuum. Passing from water to air at 49°, n₁ sinθ₁ =1.33×sin49°≈1.33×0.755=1.004>1, so sinθ₂>1 impossible, total internal reflection occurs, no refraction. Inside the focal point, a convex lens diverges rays, forming a virtual image on the same side. Beyond the focal point, the lens converges rays to a point on the opposite side, forming a real image. This transition occurs as the object crosses the focal point, changing the ray behavior. Substituting values gives Due to change from divergence to convergence, which matches expected image position and magnification from mirror/lens formula 1/f =

Ref: NCERT > Physics Book > Ray Optics > Refraction at Plane Surfaces and Snell's Law

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Reflection by Spherical Mirrors and Mirror Formula

A convex mirror of radius of curvature \( 40 \, \text{cm} \) forms an image \( 10 \, \text{cm} \) behind the mirror. Wha

**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 = (R/2) = (40/2) = 20 cm (convex mirror). Image distance: v = 10 cm (virtual image). Mirror equation: (1/v) + (1/u) = (1/f) . (1/10) + (1/u) = (1/20) ⇒ (1/u) = (1/20) - (1/10) = (1 - 2/20) = (-1/20) . u =

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

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Thin Lenses - Lens Formula, Magnification and Power

What is the primary condition under which a convex lens forms a virtual and magnified image?

**Convex lens image formation**: object beyond 2F (u>2f) real inverted diminished between F and 2F, at 2F same size at 2F, between F and 2F magnified beyond 2F, at F image at infinity, within F virtual erect magnified same side. For f=15 cm, u=30 cm=2f, m = v/u =30/30=1? Actually v=30 cm, m=-1, same size inverted. For a convex lens, a virtual and magnified image is formed when the object is placed between the focal point (F) and the optical center (O). In this position, the rays diverge after refraction, and their backward extensions converge on the same side as the object, producing a virtual,

Ref: NCERT > Physics Book > Ray Optics > Thin Lenses - Lens Formula, Magnification and Power

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