Answer
Verified
387.9k+ views
Hint: The ratio of radius, focal length, and refractive index is given. From the ratio of radii try to consider the values of the radius. Then apply the lens maker formula. And then replace the variables with the values that are given and the values that we have considered.
Formula used:
$\dfrac{1}{f}=(\mu -1)\left( \dfrac{1}{{{R}_{1}}}-\dfrac{1}{{{R}_{2}}} \right)$
Complete step by step answer:
In the question, it is given that the ratio of radii of a converging lens is 1:2
The focal length of the lens is 6cm
And the refractive index is 1.5.
Let the radius ${{R}_{1}}=R$
Then${{R}_{2}}$, must be negative, and two times of ${{R}_{1}}$, as given in the ratio,
${{R}_{2}}=-2R$.
Now applying Lens maker formula,
The formula is,
$\dfrac{1}{f}=(\mu -1)\left( \dfrac{1}{{{R}_{1}}}-\dfrac{1}{{{R}_{2}}} \right)$
$\dfrac{1}{6}=(1.5-1)\left( \dfrac{1}{R}+\dfrac{1}{2R} \right)$, (on replacing with the values given and considered)
$\Rightarrow \dfrac{1}{6}=(0.5)\left( \dfrac{3}{2R} \right)$,
$\Rightarrow \dfrac{1}{6}=\left( \dfrac{1.5}{2R} \right)$,
$\Rightarrow R=4.5cm$
${{R}_{1}}=4.5cm$.
${{R}_{2}}=9cm$.
So, the correct answer is “Option D”.
Additional Information:
When any ray of light travels parallel to a lens principal axis, and the lens converges those rays of light to its middle, that type of lens is called a converging lens. These lenses are thinner at the periphery and thicker in the middle.
Lens maker formula is a formula that gives us the relationship between focal length in terms of the refractive index and radius of the two curvatures of the lens.
Note:
In the formula, $\dfrac{1}{f}=(\mu -1)\left( \dfrac{1}{{{R}_{1}}}-\dfrac{1}{{{R}_{2}}} \right)$, ‘f’ is the focal length, ‘$\mu $’, is the refractive index and ${{R}_{1}}$ is the radius of curvature of one side of the lens and ${{R}_{1}}$ is radius of curvature of the second side of lens.
Formula used:
$\dfrac{1}{f}=(\mu -1)\left( \dfrac{1}{{{R}_{1}}}-\dfrac{1}{{{R}_{2}}} \right)$
Complete step by step answer:
In the question, it is given that the ratio of radii of a converging lens is 1:2
The focal length of the lens is 6cm
And the refractive index is 1.5.
Let the radius ${{R}_{1}}=R$
Then${{R}_{2}}$, must be negative, and two times of ${{R}_{1}}$, as given in the ratio,
${{R}_{2}}=-2R$.
Now applying Lens maker formula,
The formula is,
$\dfrac{1}{f}=(\mu -1)\left( \dfrac{1}{{{R}_{1}}}-\dfrac{1}{{{R}_{2}}} \right)$
$\dfrac{1}{6}=(1.5-1)\left( \dfrac{1}{R}+\dfrac{1}{2R} \right)$, (on replacing with the values given and considered)
$\Rightarrow \dfrac{1}{6}=(0.5)\left( \dfrac{3}{2R} \right)$,
$\Rightarrow \dfrac{1}{6}=\left( \dfrac{1.5}{2R} \right)$,
$\Rightarrow R=4.5cm$
${{R}_{1}}=4.5cm$.
${{R}_{2}}=9cm$.
So, the correct answer is “Option D”.
Additional Information:
When any ray of light travels parallel to a lens principal axis, and the lens converges those rays of light to its middle, that type of lens is called a converging lens. These lenses are thinner at the periphery and thicker in the middle.
Lens maker formula is a formula that gives us the relationship between focal length in terms of the refractive index and radius of the two curvatures of the lens.
Note:
In the formula, $\dfrac{1}{f}=(\mu -1)\left( \dfrac{1}{{{R}_{1}}}-\dfrac{1}{{{R}_{2}}} \right)$, ‘f’ is the focal length, ‘$\mu $’, is the refractive index and ${{R}_{1}}$ is the radius of curvature of one side of the lens and ${{R}_{1}}$ is radius of curvature of the second side of lens.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE