Lecture on Instruments

Introduction

• Lecture on a simple and small topic: Instruments.
• Covering Vernier Caliper, Screw Gauge, Microscope, and Telescope.
• Importance: Guaranteed question in JEE Mains, probability in JEE Advanced.
• Duration: 2-3 hours.

Vernier Caliper

• Purpose: Measures lengths smaller than 1 millimeter which a normal scale can't measure.

• Design:

  • Main Scale: Measures up to 1 millimeter.
  • Vernier Scale: Measures smaller distances (up to 0.1 millimeters).
  • External Jaws: Measure outer diameters.
  • Internal Jaws: Measure inner diameters.
  • Depth Probe: Measures depth.

• Working Principle:

  • Normal scale can measure up to 1 millimeter.
  • Vernier Caliper helps to measure distances smaller than 1 millimeter.
  • Vernier Caliper’s least count: 0.1 millimeter.

• Measurement Steps:

  1. Identify Main Scale Reading (MSR): Find the position of the zero mark of the Vernier scale on the main scale.
  2. Vernier Scale Reading (VSR): Identify which Vernier scale division aligns with any main scale division.
  3. Calculate Reading: Reading = MSR + (VSR × Least Count).

• Example:

  • If the Vernier zero is between 5mm and 6mm (MSR = 5mm), and the 7th Vernier division aligns with a main scale division (VSR = 7), then:
    • Reading = MSR + (VSR × Least Count)
    • Reading = 5mm + (7 × 0.1mm) = 5.7mm

• Zero Error:

  • Positive Zero Error: Vernier zero is to the right of the main scale zero.
  • Negative Zero Error: Vernier zero is to the left of the main scale zero.
  • Adjustment:
    • Positive Error: Subtract from the final reading.
    • Negative Error: Add to the final reading.

Screw Gauge

• Purpose: Measures even smaller distances than Vernier Caliper.

• Design:

  • Main Scale: Has divisions of 0.5 millimeters.
  • Circular Scale: Has 50 divisions.

• Working Principle:

  • 50 circular scale divisions move the main scale by 0.5 millimeters.
  • Least count = Pitch / Number of divisions on circular scale = 0.5mm / 50 = 0.01mm.

• Measurement Steps:

  1. Identify Main Scale Reading (MSR): Position of zero mark of the circular scale on the main scale.
  2. Circular Scale Reading (CSR): Identify the division on the circular scale that aligns with the main scale.
  3. Calculate Reading: Reading = MSR + (CSR × Least Count).

• Example:

  • If the zero mark of the circular scale is between 3.5mm and 4mm (MSR = 3.5mm), and the 15th circular scale division aligns with the main scale division (CSR = 15), then:
    • Reading = MSR + (CSR × Least Count)
    • Reading = 3.5mm + (15 × 0.01mm) = 3.65mm

• Zero Error:

  • Similar concept to Vernier Caliper.

Optical Instruments

Simple Microscope

• Design: Convex lens used as a magnifying glass.
• Magnification:
  • Normal Adjustment: Least strain on the eye, image at infinity.
  • Maximum Magnification: Image at the least distance of distinct vision (25 cm).
  • Formulas:
    • Normal: M = D / f
    • Maximum: M = (1 + D/f), where D = 25 cm.

Compound Microscope

• Design: Uses two lenses, objective and eyepiece.
• Magnification:
  • Normal Adjustment: Final image at infinity.
  • Maximum Magnification: Final image at the least distance of distinct vision (25 cm).
  • Formulas:
    • Normal: M = (L × D) / (f_o × f_e)
    • Maximum: M = (L / f_o) × (1 + D / f_e), where L is the tube length.

Astronomical Telescope

• Design: Uses objective lens and eyepiece.

• Magnification:

  • Normal Adjustment: Final image at infinity.
  • Maximum Magnification: Final image at the least distance of distinct vision (25 cm).
  • Formulas:
    • Normal: M = f_o / f_e
    • Maximum: M = (f_o / f_e) × (1 + D / f_e), where D = 25 cm.

• Tube Length: Sum of focal lengths of objective and eyepiece.

Closing Remarks

• These instruments are critical for precise measurements and have applications in various scientific fields.
• Ensure familiarity with reading instruments and calculating errors for success in competitive exams.