Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202523 Jan 2025Morning ShiftPhysicsRay OpticsActual

Given a thin convex lens (refractive index ₂ ), kept in a liquid (refractive index ₁, ₁ ₂ ) having radii of curvatures |R₁ | and |R₂ | . Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

Options

  1. A₁ | R ₁ | | R ₂ | ₂ ( | R ₁ |+ | R ₂ | )- ₁ | R ₂ |
  2. B₁ | R ₁ | | R ₂ | ₂ ( | R ₁ |+ | R ₂ | )- ₁ | R ₁ |
  3. C( ₂+ ₁ ) | R ₁ | ( ₂- ₁ )
  4. D₁ | R ₁ | | R ₂ | ₂ (2 | R ₁ |+ | R ₂ | )- ₁ | R ₁ | | R ₂ |

Correct answer

A. ₁ | R ₁ | | R ₂ | ₂ ( | R ₁ |+ | R ₂ | )- ₁ | R ₂ |

Step-by-step solution

aligned & 1 f _ eq = 2 f _ L - 1 f _ m & f _ m =- | R ₂ | 2 & 1 f _ L = ( ₂ ₁ -1 ) ( 1 R ₁ + 1 R ₂ ) aligned aligned & 1 f _ eq =2 ( ₂- ₁ ₁ ) ( R ₁+ R ₂ R ₁ R ₂ )+ 2 R ₂ & = 2 R ₂ [ ( ₂- ₁ ) ( R ₁+ R ₂ )+ ₁ R ₁ ₁ R ₁ ] & = 2 R ₂ [ ₂ R ₁+ ₂ R ₂- ₁ R ₁- ₁ R ₂+ ₁ R ₁ ₁ R ₁ ] & 1 f _ eq = 2 [ ₂ R ₁+ ₂ R ₂- ₁ R ₂ ] ₁ R ₁ R ₂ aligned For same size of image aligned & u =2 f & u = ₁ R ₁ R ₂ ₂ R ₁+ ₂ R ₂- ₁ R ₂ aligned

Practice Ray Optics on Quantrex Academy →

More from Ray Optics

A double convex lens made of glass of refractive index 1.5 and radii of curvature of the curved surfaces 20 cm each is immersed in a liquid of refractive index n_L . The correct pl 2026A beam of polychromatic light passes through a thin prism of prism angle 6^ . The refractive index of the material of the prism varies with wavelength ( ) as n( ) = + ^2 , where = 2026Consider two isosceles prisms 1 and 2 with prism angles A₁ and A₂ and refractive indices n₁ and n₂ , respectively, as shown in the figure. The faces a₁ b₁ and a₂ b₂ are parallel to 2026A thin biconvex lens is prepared from the glass ( =1.5 ) both curved surfaces of which have equal radii of 20 cm each. Left side surface of the lens is silvered from outside to mak 2026Light ray incident along a vector AO ( AO = 2 i -3 j ) emerges out along vector OB ( OB = C i -4 j ) as shown in the figure below. The value of C is ________. 2026Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is __________. 2026A concave mirror of focal length 10 cm forms an image which is double the size of object when the object is placed at two different positions. The distance between the two position 2026A spherical interface lens of radius R separates two media of refractive indices 1 and 1.4 respectively as shown in the figure below. A point source is placed at a distance of 4R i 2026 Full Ray Optics list All JEE Main PYQs