The plane face of a plano-convex lens is silvered. If μ be the refractive index and R, the radius of curvature of the curved surface, then the system will behave like a concave mirror of curvature.

μR

R²/μ

R/(μ -1)

[(μ + 1)/(μ-1)]R

Solution

R/(μ -1)

When an object is placed in front of such a lens, the rays first of all refracted from the convex surface, then refract from the polished plane surface and again refracts from convex surface. If f_l and f_m be the focal lengths of lens (convex surface) and mirror (plane polished surface) respectively, then effective focal length F is given by

$\frac{1}{F} = \frac{1}{f_{l}} + \frac{1}{f_{m}} + \frac{1}{f_{l}} = \frac{2}{f_{l}} + \frac{1}{f_{m}} = \frac{2}{f_{l}} (∵ f_{m} = \frac{R}{2} = \infty) \frac{1}{f_{l}} = (μ - 1) \frac{1}{R} ∴ \frac{1}{F} = \frac{2 (μ - 1)}{R} or F = \frac{R}{2 (μ - 1)} Or R = 2 F = \frac{R}{(μ - 1)}$

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Ray Optics And Optical Instruments

The plane face of a plano-convex lens is silvered. If μ be the refractive index and R, the radius of curvature of the curved surface, then the system will behave like a concave mirror of curvature.

μR

R²/μ

R/(μ -1)

[(μ + 1)/(μ-1)]R

Some More Questions From Ray Optics and Optical Instruments Chapter

An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distance are measured by

Two lenses of power -15D and +5D are in contact with each other. The focal length of the combination is

The angle of incidence at which reflected light totally polarized for reflection from air to glass (refractive index n), is

If θ1 and θ2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip θ is given by

A thin prism having refracting angle 10° is made of glass of refractive index 1.42. This prism is combined with another thin prism of a glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of second prism should be

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Ray Optics And Optical Instruments

The plane face of a plano-convex lens is silvered. If μ be the refractive index and R, the radius of curvature of the curved surface, then the system will behave like a concave mirror of curvature. μR R2/μ R/(μ -1) [(μ + 1)/(μ-1)]R

Some More Questions From Ray Optics and Optical Instruments Chapter

An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distance are measured by

Two lenses of power -15D and +5D are in contact with each other. The focal length of the combination is

The angle of incidence at which reflected light totally polarized for reflection from air to glass (refractive index n), is

If θ1 and θ2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip θ is given by

A thin prism having refracting angle 10° is made of glass of refractive index 1.42. This prism is combined with another thin prism of a glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of second prism should be

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The plane face of a plano-convex lens is silvered. If μ be the refractive index and R, the radius of curvature of the curved surface, then the system will behave like a concave mirror of curvature.

μR

R²/μ

R/(μ -1)

[(μ + 1)/(μ-1)]R