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Ray Optics and Optical Instruments appeared 63 times across 3 years — 7.3% of Physics. This question is from Lens Maker's Formula.

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A bi-convex lens has radius of curvature of both the surfaces same as 1/6 cm. If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides ( R₁ ≠ R₂ ), without any change in lens power then possible combination of R₁ and R₂ is:

Solution & Explanation

Related Formula

Lens Maker's Formula:

(1)/(f) = (μ - 1) ((1)/(R₁) - (1)/(R₂))

For a bi-convex lens of equal radii (R₁ = +R, R₂ = -R):

(1)/(f) = (μ - 1) (2)/(R)

Power P ∝ (1)/(f).

Core Logic

For the initial lens:

  • R = (1)/(6) cm
  • (1)/(f₁) = (μ - 1) (2)/(1/6) = 12 (μ - 1)

    • For the replacement lens (R₁ = +R₁, R₂ = -R₂):

(1)/(f₂) = (μ - 1) ((1)/(R₁) + (1)/(R₂))

Since power must be preserved (f₁ = f₂):

(1)/(R₁) + (1)/(R₂) = (2)/(R) = 12 cm⁻¹

We need to find a combination where the sum of the reciprocals of the radii equals 12.

Step 1: Verify the options

Let's check each choice:

  • Option (1): R₁ = (1)/(3), R₂ = (1)/(3):
(1)/(1/3) + (1)/(1/3) = 3 + 3 = 6 ≠ 12
  • Option (2): R₁ = (1)/(5), R₂ = (1)/(7):
(1)/(1/5) + (1)/(1/7) = 5 + 7 = 12 (Correct Combination)
  • Option (3): R₁ = (1)/(3), R₂ = (1)/(7):
(1)/(1/3) + (1)/(1/7) = 3 + 7 = 10 ≠ 12
  • Option (4): R₁ = (1)/(6), R₂ = (1)/(9):
(1)/(1/6) + (1)/(1/9) = 6 + 9 = 15 ≠ 12

Thus, only Option (2) meets the physical conditions.

Pattern Recognition

Sees: Equivalent thin lens power with modified surfaces. Trap: Neglecting sign convention for the second spherical surface during substitution. Shortcut: If the radii are of the form 1/n, then the sum of n₁ + n₂ must equal 2 × ninitial. Since initial n = 6, 2 × 6 = 12. The only pairing whose denominators add up to 12 is 5 + 7.

Chapter Mix

Class 12 Physics: Ray Optics and Optical Instruments

Reference Study Guides

Ray Optics And Optical Instruments

More Ray Optics and Optical Instruments Previous-Year Questions — Page 8

Q20 jee_main_2025_28_jan_morning Prism and Dispersion
A thin prism P₁ with angle 4° made of glass having refractive index 1.54, is combined with another thin prism P₂ made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism P₂ in degrees is
  • A. 4
  • B. 3
  • C. 16/3
  • D. 1.5

Solution

Related Formula
δ = (μ - 1)A
Core Logic

To achieve dispersion without deviation, the net deviation produced by the prism combination must be zero:

δₙₑₜ = 0 (μ₁ - 1)A₁ - (μ₂ - 1)A₂ = 0

Substituting the given parameters into the equation:

(1.54 - 1) · 4° - (1.72 - 1)A₂ = 0 0.54 · 4 = 0.72 · A₂ A₂ = (2.16)/(0.72) = 3°
Step 1: Final Angle Value

The required angle for the second thin prism is 3°, which matches option (2).

Pattern Recognition

For zero deviation conditions using thin components, balance the deviation equations directly: (μ-1)A = (μ'-1)A'.

Chapter Mix

Class 12 Physics: Ray Optics and Optical Instruments

Q18 jee_main_2025_03_april_morning Lens Maker's Formula
The radii of curvature for a thin convex lens are 10~cm and 15~cm respectively. The focal length of the lens is 12~cm. The refractive index of the lens material is:
  • A. 1.2
  • B. 1.4
  • C. 1.5
  • D. 1.8

Solution

Related Formula

Lens Maker's Formula:

(1)/(f) = (μ - 1) ((1)/(R₁) - (1)/(R₂))

where, f = focal length of the lens, μ = refractive index of the material, R₁, R₂ = radii of curvature with standard Cartesian sign convention.

Core Logic

For a thin bi-convex lens, using standard coordinate conventions:

  • R₁ = +10~cm (positive since first surface centers to the right of light trajectory),
  • R₂ = -15~cm (negative since second surface centers to the left),
  • Focal length f = +12~cm.
Step 1: Substituting in the Equation

Substitute the values into Lens Maker's formula:

(1)/(12) = (μ - 1) ((1)/(10) - (1)/(-15)) (1)/(12) = (μ - 1) ((1)/(10) + (1)/(15)) (1)/(12) = (μ - 1) ((3 + 2)/(30)) (1)/(12) = (μ - 1) ((5)/(30)) = (μ - 1) ((1)/(6)) μ - 1 = (6)/(12) = 0.5 μ = 1.5
Pattern Recognition

Convex lenses always have opposite signs for R₁ and R₂. The term ((1)/(R₁) - (1)/(R₂)) is additive: ((1)/(|R₁|) + (1)/(|R₂|)).

Chapter Mix

Class 12 Physics: Ray Optics and Optical Instruments

Q20 jee_main_2025_03_april_morning Minimum Deviation in Prism
Consider following statements for refraction of light through prism, when angle of deviation is minimum. (A) The refracted ray inside prism becomes parallel to the base. (B) Larger angle prisms provide smaller angle of minimum deviation. (C) Angle of incidence and angle of emergence becomes equal. (D) There are always two sets of angle of incidence for which deviation will be same except at minimum deviation setting. (E) Angle of refraction becomes double of prism angle. Choose the correct answer from the options given below.
  • A. A, C and D Only
  • B. B, C and D Only
  • C. A, B and E Only
  • D. B, D and E Only

Solution

Related Formula

For a prism of angle A:

  • Deviation: δ = i + e - A
  • Minimum deviation δmin occurs when:
i = e and r₁ = r₂ = (A)/(2)
  • Under minimum deviation, the ray inside an equilateral/isosceles prism travels symmetrically, making it parallel to the prism base.
Core Logic

Let's check the validity of each statement:

  • Statement (A): The refracted ray inside the prism becomes parallel to the base at minimum deviation. (True for symmetric prisms)
  • Statement (B): Larger angle prisms provide smaller minimum deviation. By minimum deviation equation:
μ = ( A+δmin2) ((A)/(2))

As A increases, δmin generally increases, not decreases. (False)

  • Statement (C): Angle of incidence i and angle of emergence e become equal (i = e) during the minimum deviation state. (True)
  • Statement (D): The δ-i curve is asymmetric and parabolic-like; for any deviation δ > δmin, there are always exactly two different incident angles (i and e) that yield the same deviation, except at the minimum deviation point (which has a single unique value). (True)
  • Statement (E): Angle of refraction r = A/2, which is half of the prism angle, not double. (False)
Step 1: Conclusion

Since statements A, C, and D are true, the correct option is (1).

Pattern Recognition

Review the classic parabolic shape of the deviation vs. angle of incidence (δ-i) graph. Notice that any horizontal line above the minimum point intersects twice (representing i and e for that deviation). Minimum deviation is the unique local minimum, where i = e and r₁ = r₂ = A/2.

Chapter Mix

Class 12 Physics: Ray Optics and Optical Instruments: Refraction through Prism

Q19 jee_main_2025_04_april_evening Spherical Mirrors
A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is :
  • A. 45 cm
  • B. 7.5 cm
  • C. 22.5 cm
  • D. 15 cm

Solution

Related Formula

Mirror Formula:

(1)/(v) + (1)/(u) = (1)/(f)
Core Logic

For the convex mirror, u = -30 cm and f = +30 cm.

(1)/(v) - (1)/(30) = (1)/(30) (1)/(v) = (2)/(30) v = +15 cm

So, the convex mirror forms a virtual image 15 cm behind its surface.

Step 1: Align Plane Mirror Image

The total distance from the object to the image location is 30 + 15 = 45 cm. For a plane mirror to create an image at this same exact location, it must be placed precisely midway between the object and the image. Distance from object to plane mirror:

d = (45)/(2) = 22.5 cm

Therefore, the clearance distance between the convex mirror and the plane mirror surface is:

Distance = 30 - 22.5 = 7.5 cm
Pattern Recognition

Coinciding images imply identical coordinate endpoints. Calculate the convex position explicitly, find the total path length from the real source object, and slice it in half for the plane mirror location.

Chapter Mix

Class 12 Physics: Ray Optics and Optical Instruments

Q jee_main_2025_04_april_morning Spherical Mirrors and Magnification
When an object is placed 40~cm away from a spherical mirror an image of magnification (1)/(2) is produced. To obtain an image with magnification of (1)/(3), the object is to be moved:
  • A. 40 cm away from the mirror.
  • B. 80 cm away from the mirror.
  • C. 20 cm towards the mirror.
  • D. 20 cm away from the mirror.

Solution

Related Formula

Magnification formula for a spherical mirror in terms of focal length f and object distance u:

m = (f)/(f - u)
Core Logic

Case 1: Given u₁ = -40~cm and m₁ = (1)/(2):

(1)/(2) = (f)/(f - (-40)) f + 40 = 2f f = +40~cm

Since f > 0, the optical element is a convex mirror forming a virtual, erect, and diminished image (0 < m < 1).

Step 1: Calculate New Object Position

Case 2: To achieve a magnification of m₂ = (1)/(3):

(1)/(3) = (40)/(40 - u₂) 40 - u₂ = 120 u₂ = -80~cm
Step 2: Determine Distance Shift
  • Initial object position: u₁ = -40~cm
  • Final object position: u₂ = -80~cm
Shift = |u₂| - |u₁| = 80 - 40 = 40~cm away from the mirror
Pattern Recognition

For a convex mirror, images are always virtual, erect, and diminished. As the object is shifted farther away from the mirror (u → -∞), the magnification decreases toward zero.

Chapter Mix

Class 12 Physics: Ray Optics and Optical Instruments

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