A monochromatic ray of light travels through a glass slab and water .| PGMN Solutions

A monochromatic ray of light travels through a glass slab and water column. The number of waves in glass slab of thickness 4 cm is the same as in water column of height 5 cm. If refractive index of glass is five by three, then refractive index of water is:
(A) 1.33 (B) 1.30 (C) 1.25 (D) 1.10

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🚀 Step-by-Step Solution to Solve This Question 🚀
📌 Chapter: Wave Optics
📌 Topic: Wavelength and Refractive Index in Different Mediums

🔹 Step 1: Understand the concept of wave count
The number of waves in a medium is proportional to the optical path length, which is the product of refractive index and actual length of the medium.

🔹 Step 2: Apply equality condition
Given that the number of waves in the glass and water are the same, we equate the optical path lengths:
Refractive index of glass × Thickness of glass = Refractive index of water × Height of water

🔹 Step 3: Substitute values
Refractive index of glass is five by three
Glass thickness = 4 cm
Water height = 5 cm
Let refractive index of water be x
So, (5 by 3) × 4 = x × 5
This gives x = (5 × 4) / (3 × 5) = 4 / 3 = 1.33

🔹 Step 4: Conclude with the correct option
The calculated refractive index of water is 1.33

✅ Final Answer: (A) 1.33 🚀
🔥 Pro Tip: When number of waves is the same in different media, compare the product of refractive index and length directly—this is called the optical path.

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