Question

★For physics Newton★

Ravi is given lenses with powers + 5 D, - 5 D, + 10 D,- 10 D and -20 D. Considering a pair of lenses at a time, which two lenses will he select to have a combination of total focal length when two lenses are kept in contact in each case:
i. -10 cm
ii. 20 cm
iii. -20 cm​

Answer 1

Answer :-

The required combination of lenses are :-

(i) +10 D and -20 D

(ii) -5 D and +10 D

(iii) +5 D and -10 D .

Explanation :-

When power of a lens is in 'Dioptre' and focal length is in 'cm', then relationship between the two is given by :-

P = 100/f

Also, for 2 lenses in contact , we have :-

P = P₁ + P₂

For number (i) :-

⇒ P = 100/(-10)

⇒ P = -10 D

⇒ -10 = 10 + (-20)

→ P₁ = 10 D

→ P₂ = -20D

For Number (ii) :-

⇒ P = 100/20

⇒ P = 5 D

⇒ 5 = -5 + 10

→ P₁ = -5 D

→ P₂ = 10 D

For number (iii) :-

⇒ P = 100/(-20)

⇒ P = -5 D

⇒ -5 = 5 + (-10)

→ P₁ = 5 D

→ P₂ = -10 D

Answer 2

Given:-

• Ravi is given lenses with powers + 5 D, - 5 D, + 10 D,- 10 D and -20 D.

To Find:-

• Combination of the lenses

Formula Used:-

• ${\boxed{\bf{Power=\dfrac{100}{f}}}}$ (in cm)

Solution:-

As we know, the two lenses have to be in contact. So,

i) -10 cm

$\sf :\implies\: P = \dfrac{100}{-10}$

$\sf :\implies\: P = -10\:D$

Now, we have to check which combination is satisfying

$\sf :\implies\: -20D + 10D = -10D$

So, First combination is 10D and -20D.

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ii) 20 cm

$\sf :\implies\: P = \dfrac{100}{20}$

$\sf :\implies\: P = 5\:D$

Now, we have to check which combination is satisfying

$\sf :\implies\: -5D + 10D = 5D$

So, second combination is 10D and -5D.

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i) -20 cm

$\sf :\implies\: P = \dfrac{100}{-20}$

$\sf :\implies\: P = -5\:D$

Now, we have to check which combination is satisfying

$\sf :\implies\: -10D + 5D = -5D$

So, third combination is 5D and -10D.

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