Refraction at Spherical Surfaces and Lens Maker's Formula

Refraction at Spherical Surfaces and Lens Maker's Formula

An object is at a depth of \( 19.95 \, \text{cm} \) in a medium with refractive index \( 1.5 \). What is the apparent de

**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. Apparent depth = (real depth/n) . Real depth = 19.95 cm , n = 1.5 . Apparent depth = (19.95/1.5) = 13.3 cm . Substituting values gives 13.3 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 conventions and refraction principles.

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

View Details

Refraction at Spherical Surfaces and Lens Maker's Formula

What optical principle allows a prism to be used as a reflector in optical devices?

**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. Prisms reflect light via total internal reflection when the angle of incidence exceeds the critical angle at the prism’s internal surfaces. This property, dependent on the prism’s refractive index and angle, enables efficient reflection without loss, as seen in devices like binoculars. Substituting values gives Total internal reflection, 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

View Details

Refraction at Spherical Surfaces and Lens Maker's Formula

What is the critical angle for a diamond (\( n = 2.42 \)) to water (\( n = 1.33 \)) interface?

**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. Critical angle: sin i_c = (n₂/n₁) . Diamond ( n₁ = 2.42 ), water ( n₂ = 1.33 ). sin i_c = (1.33/2.42) ≈ 0.55 . i_c = sin⁻¹(0.55) ≈ 33.4° . Substituting values gives 33°, 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 conventions and refraction principles.

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

View Details

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

View Details

Refraction at Spherical Surfaces and Lens Maker's Formula

A lens has a power of \( +3 \, \text{D} \). What is its focal length in centimeters?

**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. Power: P = (1/f) (in meters). P = +3 D ⇒ 3 = (1/f) ⇒ f = (1/3) ≈ 0.333 m ≈ 33.3 cm . Substituting values gives 33 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 conventions and refraction principles.

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

View Details

Refraction at Spherical Surfaces and Lens Maker's Formula

In optical fibers, what ensures that light remains confined within the core during transmission?

**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. In optical fibers, the core has a higher refractive index than the cladding, enabling total internal reflection. When light strikes the core-cladding boundary at an angle greater than the critical angle, it reflects back into the core, ensuring confinement and minimal loss. Substituting values gives Higher refractive index of core than cladding, 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

View Details

Refraction at Spherical Surfaces and Lens Maker's Formula

A simple microscope uses a lens of focal length \( 8 \, \text{cm} \). What is the magnification when the image is at inf

**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. Magnification at infinity: m = (D/f) . D = 25 cm , f = 8 cm . m = (25/8) = 3.125 . Substituting values gives 3.1, 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 conventions and refraction principles.

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

View Details

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

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

View Details

Refraction at Spherical Surfaces and Lens Maker's Formula

A double convex lens has radii of curvature \( 30 \, \text{cm} \) and \( -30 \, \text{cm} \) with refractive index \( 1.

**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. Lens maker’s formula: (1/f) = (n - 1) ( (1/R₁) - (1/R₂) ) . n = 1.6 , R₁ = 30 cm , R₂ = -30 cm . (1/f) = (1.6 - 1) ( (1/30) - (1/-30) ) = 0.6 ( (1/30) + (1/30) ) = 0.6 × (2/30) = (1.2/30) = (1/25) . f = 25 cm . Substituting values gives 25 cm, which matches expected image position and

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

View Details

Refraction at Spherical Surfaces and Lens Maker's Formula

What is the critical angle for a crown glass (\( n = 1.52 \)) to air interface?

**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. Critical angle: sin i_c = (n₂/n₁) . Crown glass ( n₁ = 1.52 ), air ( n₂ = 1 ). sin i_c = (1/1.52) ≈ 0.658 . i_c = sin⁻¹(0.658) ≈ 41.1° . Substituting values gives 41°, 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 conventions and refraction principles.

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

View Details

Refraction at Spherical Surfaces and Lens Maker's Formula

A double convex lens of refractive index \( 1.5 \) has radii of curvature \( 18 \, \text{cm} \) and \( -18 \, \text{cm}

**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. Lens maker’s formula: (1/f) = (n - 1) ( (1/R₁) - (1/R₂) ) . n = 1.5 , R₁ = 18 cm , R₂ = -18 cm . (1/f) = (1.5 - 1) ( (1/18) - (1/-18) ) = 0.5 ( (1/18) + (1/18) ) = 0.5 × (2/18) = (1/18) . f = 18 cm . Substituting values gives 18 cm, which matches expected image

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

View Details

Refraction at Spherical Surfaces and Lens Maker's Formula

A converging beam meets a convex lens (\( f = 20 \, \text{cm} \)) \( 8 \, \text{cm} \) before the convergence point. Wha

**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. Object distance: u = -8 cm (virtual object). Focal length: f = 20 cm . Lens formula: (1/v) - (1/-8) = (1/20) ⇒ (1/v) + (1/8) = (1/20) . (1/v) = (1/20) - (1/8) = (2 - 5/40) = (-3/40) . v = -(40/3) ≈ -13.33 cm (13.33 cm to the left). Substituting values gives 13.3 cm, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v

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

View Details