Question

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Qno:-33

Answer 1

QUESTION :

The radius of the 5 th Newton ring is 3 mm , when light of wavelength 4×10⁻⁴ m is used . Find the radius of curvature of the lens used .

A) 0.8 mm

B) 0.5 cm

C) 0.5 mm

D) 0.8 cm

ANSWER :

Given :

Radius of the n th ring = 3 mm .

Wavelength of light = 4×10⁻⁴ m

1 m = 10² cm ⇒ 10²×10 mm ⇒ 10³ mm .

4 × 10⁻⁴m ⇒ 4 × 10⁻⁴ × 10³ mm

⇒ 4 × 10⁻¹ mm

⇒ 0.4 mm

Number of rings = 5 .

Let the radius of curvature be R .

Using the formula :

Radius of nth ring = √[ wavelength × radius of ring ( number of rings - 1/2 ) ]

⇒ 3 mm = √[ 0.4 mm × R ( N - 1/2 ) ]

⇒ 3 mm = √[ 0.4 R × ( 5 - 1/2 ) ]

⇒ 3 mm = √[ 0.4 R × ( 10 - 1 ) / 2 ]

⇒ 3 mm = √[ 0.4 R × 9/2 ]

⇒ 3 mm = √[ 0.2 R × 9 ]

⇒ 3 mm = √( 1.8 R )

⇒ 9 mm² = 1.8 R

⇒ R = ( 9/1.8 )

⇒ R = 5 mm

5 mm is equivalent to 0.5 cm .

Hence the radius of curvature of the lens is 0.5 cm .

OPTION B is correct !

Answer 2

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