Class 12 Physics Ray Optics and Optical Instruments Notes

9.1 Introduction

Ray optics, also called geometric optics, studies light propagation in straight lines. It explains reflection, refraction, and the working of optical devices such as mirrors, lenses, microscopes, and telescopes.

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9.2 Reflection of Light by Spherical Mirrors

• Spherical mirrors: Concave and convex mirrors.
• Mirror equation:

$$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$f1​=u1​+v1​

• Magnification:

$$m = \frac{h_i}{h_o} = -\frac{v}{u}$$m=ho​hi​​=−uv​

• Focal length (f):

$$f = \frac{R}{2}$$f=2R​

• R = radius of curvature
• Sign convention: Real is positive for distances in the same direction as the incident light.

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9.3 Refraction

• Refraction is the bending of light at the interface of two media.
• Snell’s law:

$$n_1 \sin\theta_1 = n_2 \sin\theta_2$$n1​sinθ1​=n2​sinθ2​

• n = refractive index
• Light bends toward the normal in a denser medium.

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9.4 Total Internal Reflection

• Occurs when light moves from denser to rarer medium at an angle greater than the critical angle (θc\theta_cθc​).

$$\sin\theta_c = \frac{n_2}{n_1}$$sinθc​=n1​n2​​

• Applications:
  • Optical fibers
  • Periscopes
  • Light pipes

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9.5 Refraction at Spherical Surfaces and by Lenses

• Lens formula:

$$\frac{1}{f} = \frac{1}{v} – \frac{1}{u}$$f1​=v1​−u1​

• Lens maker’s formula:

$$\frac{1}{f} = (n-1) \left( \frac{1}{R_1} – \frac{1}{R_2} \right)$$f1​=(n−1)(R1​1​−R2​1​)

• Convex and concave lenses bend light to form images.
• Magnification:

$$m = \frac{h_i}{h_o} = \frac{v}{u}$$m=ho​hi​​=uv​

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9.6 Refraction through a Prism

• Prism deviates light due to refraction at two surfaces.
• Angle of deviation (δ):

$$\delta = i_1 + i_2 – A$$δ=i1​+i2​−A

• A = prism angle
• Minimum deviation (δmδ_mδm​) used to measure refractive index of prism.

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9.7 Optical Instruments

1. Microscope
   • Uses two lenses: objective and eyepiece.
   • Magnifies small objects for detailed study.
2. Telescope
   • Used for observing distant objects.
   • Refracting telescope: Convex lenses
   • Reflecting telescope: Concave mirror
3. Other instruments
   • Spectrometer, camera, magnifying glass

• Principle: Uses refraction and lens formulas to form magnified images.