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NCERT Exemplar · Q27

Q.A myopic adult has a far point at 0.1 m. His power of accomodation is 4 diopters.

(i) What power lenses are required to see distant objects?
(ii) What is his near point without glasses?
(iii) What is his near point with glasses? (Take the image distance from the lens of the eye to the retina to be 2 cm.)
Gujarat GsebSubjective· 3mImportance★★★★★
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A −10 D-10\ \text{D} diverging lens corrects the distant vision; without glasses the near point lies at 114 m≈7.1 cm\tfrac{1}{14}\ \text{m} \approx 7.1\ \text{cm}, and with the glasses it moves out to the normal 0.25 m0.25\ \text{m} (25 cm25\ \text{cm}).

Data: far point =0.1 m= 0.1\ \text{m}; power of accommodation =4 D= 4\ \text{D}; image distance eye-lens to retina v=2 cm=0.02 mv = 2\ \text{cm} = 0.02\ \text{m}.

(i) Lens to see distant objects

A myopic eye focuses parallel light in front of the retina; the correcting lens must make an object at infinity appear at the far point. With u=∞u = \infty and v=−0.1 mv = -0.1\ \text{m} (virtual, on the object side):

P=1v−1u=1−0.1−0=−10 D.P = \frac{1}{v} - \frac{1}{u} = \frac{1}{-0.1} - 0 = -10\ \text{D}.

So a diverging lens of power −10 D-10\ \text{D} (focal length −10 cm-10\ \text{cm}) is required.

(ii) Near point without glasses

Treat the eye as a single lens forming the image on the retina, v=+0.02 mv = +0.02\ \text{m}. When relaxed it is focused on the far point (u=−0.1 mu = -0.1\ \text{m}):

Prelaxed=1v−1u=10.02−1−0.1=50+10=60 D.P_{\text{relaxed}} = \frac{1}{v} - \frac{1}{u} = \frac{1}{0.02} - \frac{1}{-0.1} = 50 + 10 = 60\ \text{D}.

At maximum accommodation the eye adds 4 D4\ \text{D}:

Pmax⁡=60+4=64 D.P_{\max} = 60 + 4 = 64\ \text{D}.

The near point is the closest object still imaged on the retina:

Pmax⁡=1v−1un⇒64=50−1un⇒1un=−14⇒un=−114 m≈−0.071 m.P_{\max} = \frac{1}{v} - \frac{1}{u_n} \Rightarrow 64 = 50 - \frac{1}{u_n} \Rightarrow \frac{1}{u_n} = -14 \Rightarrow u_n = -\frac{1}{14}\ \text{m} \approx -0.071\ \text{m}.

So the unaided near point is about 7.1 cm7.1\ \text{cm} from the eye.

(iii) Near point with glasses …

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