In a microscope the objective is having focal length f_0 = 2text cm and eye-piece is having focal length f_e = 4text cm. The tube length is 32 cm. The magnification produced by this microscope for normal adjustment is ____.

Numerical Answer Type:
Enter a numerical value Answer: 100 to 100 +4 marks

Solution & Explanation

### Related Formula m approx fracLf_0 times fracDf_e ### Core Logic For a compound microscope in normal adjustment (image formed at infinity), the magnifying power is given by the standard approximation: m simeq fracl Df_0 f_e where l is the tube length, D = 25text cm is the least distance of distinct vision. ### Step 1: Substitute Values Given values: l = 32text cm f_0 = 2text cm f_e = 4text cm D = 25text cm (standard assumption when not given) m = frac322 times frac254 m = 16 times frac254 = 4 times 25 = 100
Microscope solution diagram for Q50 - JEE Main 2026 Morning
Microscope solution diagram for Q50 - JEE Main 2026 Morning
### Pattern Recognition Compound microscope formulas: Normal adjustment to image at infty, m = (L/f_0)(D/f_e). Image at near point D, m = (L/f_0)(1 + D/f_e). Default to standard approximation when given tube length. ### Evaluation Rubric / Model Answer null ### 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 10

Q34 jee_main_2024_31_jan_morning Prism Deviation
The refractive index of a prism with apex angle A is cot(A/2). The angle of minimum deviation is :
  • A. delta_mathrmm = 180^circ - A
  • B. delta_mathrmm = 180^circ - 3A
  • C. delta_mathrmm = 180^circ - 4A
  • D. delta_mathrmm = 180^circ - 2A

Solution

### Related Formula mu = fracsinleft(fracA + delta_m2right)sinleft(fracA2right) ### Core Logic Given that the refractive index mu = cotleft(fracA2right). Substituting this into the prism formula: cotleft(fracA2right) = fracsinleft(fracA + delta_m2right)sinleft(fracA2right) fraccosleft(fracA2right)sinleft(fracA2right) = fracsinleft(fracA + delta_m2right)sinleft(fracA2right) Equating the numerators: cosleft(fracA2right) = sinleft(fracA + delta_m2right) We can rewrite cosine in terms of sine: sinleft(fracpi2 - fracA2right) = sinleft(fracA + delta_m2right) ### Step 2: Solve for Deviation Comparing the angles inside the sine functions: fracpi2 - fracA2 = fracA2 + fracdelta_m2 Multiply the entire equation by 2: pi - A = A + delta_m delta_m = pi - 2A Converting radians to degrees: delta_m = 180^circ - 2A ### Pattern Recognition Whenever refractive index mu = cot(A/2), the relation sin(90^circ - A/2) strictly matches the prism sine equation, meaning minimum deviation delta_m is always 180^circ - 2A. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Ray Optics And Optical Instruments

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