Spherical Surface and Lenses, Lens Formula, Magnification, Combination of Lens.
Ray Optics

282466 The focal length in air of a thin lens made of glass of refractive index 1.5 is \(L\) when immersed in water (refractive index \(=4 / 3\) ), its focal length becomes

1 \(\frac{-\mathrm{L}}{4}\)
2 \(\frac{3 \mathrm{~L}}{4}\)
3 \(4 \mathrm{~L}\)
4 \(\frac{4 \mathrm{~L}}{3}\)
Ray Optics

282457 Two thin lenses have a combined power of +9 D. When they are separated by a distance of 20 \(\mathrm{cm}\), their equivalent power becomes \(+\frac{27}{5} \mathrm{D}\), then their individual powers are

1 \(6 \mathrm{D}\) and \(3 \mathrm{D}\)
2 \(6 \mathrm{D}\) and \(4 \mathrm{D}\)
3 \(9 \mathrm{D}\) and \(3 \mathrm{D}\)
4 \(9 \mathrm{D}\) and \(6 \mathrm{D}\)
Ray Optics

282458 A light beam parallel to axis is incident on the system of four convex lenses \(A, B, C\) and \(D\). Focal lengths of \(A, B, C\) and \(D\) are \(30 \mathrm{~cm}, 10\) \(\mathrm{cm}, 30 \mathrm{~cm}\) and \(10 \mathrm{~cm}\), respectively as shown. Here, fixed distance \(B C=20 \mathrm{~cm}\). What should be the distance between the lens \(A\) and lens \(D\) so that after refractions, rays will be parallel to axis in regions I, III and V?
![original image](https://cdn.mathpix.com/snip/images/DRWKAYScknpSM6uKgx7wRDMGIC_53Fp7NbBd27zcKBs.original.fullsize.png)

1 \(40 \mathrm{~cm}\)
2 \(100 \mathrm{~cm}\)
3 \(80 \mathrm{~cm}\)
4 \(20 \mathrm{~cm}\)
Ray Optics

282459 The distance between a convex lens and a plane mirror is \(10 \mathrm{~cm}\). The parallel rays incident on the convex lens, after reflection from the mirror, form image at the optical centre of the lens. Then the focal length of the lens is

1 \(10 \mathrm{~cm}\)
2 \(20 \mathrm{~cm}\)
3 \(30 \mathrm{~cm}\)
4 \(25 \mathrm{~cm}\)
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Ray Optics

282466 The focal length in air of a thin lens made of glass of refractive index 1.5 is \(L\) when immersed in water (refractive index \(=4 / 3\) ), its focal length becomes

1 \(\frac{-\mathrm{L}}{4}\)
2 \(\frac{3 \mathrm{~L}}{4}\)
3 \(4 \mathrm{~L}\)
4 \(\frac{4 \mathrm{~L}}{3}\)
Ray Optics

282457 Two thin lenses have a combined power of +9 D. When they are separated by a distance of 20 \(\mathrm{cm}\), their equivalent power becomes \(+\frac{27}{5} \mathrm{D}\), then their individual powers are

1 \(6 \mathrm{D}\) and \(3 \mathrm{D}\)
2 \(6 \mathrm{D}\) and \(4 \mathrm{D}\)
3 \(9 \mathrm{D}\) and \(3 \mathrm{D}\)
4 \(9 \mathrm{D}\) and \(6 \mathrm{D}\)
Ray Optics

282458 A light beam parallel to axis is incident on the system of four convex lenses \(A, B, C\) and \(D\). Focal lengths of \(A, B, C\) and \(D\) are \(30 \mathrm{~cm}, 10\) \(\mathrm{cm}, 30 \mathrm{~cm}\) and \(10 \mathrm{~cm}\), respectively as shown. Here, fixed distance \(B C=20 \mathrm{~cm}\). What should be the distance between the lens \(A\) and lens \(D\) so that after refractions, rays will be parallel to axis in regions I, III and V?
![original image](https://cdn.mathpix.com/snip/images/DRWKAYScknpSM6uKgx7wRDMGIC_53Fp7NbBd27zcKBs.original.fullsize.png)

1 \(40 \mathrm{~cm}\)
2 \(100 \mathrm{~cm}\)
3 \(80 \mathrm{~cm}\)
4 \(20 \mathrm{~cm}\)
Ray Optics

282459 The distance between a convex lens and a plane mirror is \(10 \mathrm{~cm}\). The parallel rays incident on the convex lens, after reflection from the mirror, form image at the optical centre of the lens. Then the focal length of the lens is

1 \(10 \mathrm{~cm}\)
2 \(20 \mathrm{~cm}\)
3 \(30 \mathrm{~cm}\)
4 \(25 \mathrm{~cm}\)
Ray Optics

282466 The focal length in air of a thin lens made of glass of refractive index 1.5 is \(L\) when immersed in water (refractive index \(=4 / 3\) ), its focal length becomes

1 \(\frac{-\mathrm{L}}{4}\)
2 \(\frac{3 \mathrm{~L}}{4}\)
3 \(4 \mathrm{~L}\)
4 \(\frac{4 \mathrm{~L}}{3}\)
Ray Optics

282457 Two thin lenses have a combined power of +9 D. When they are separated by a distance of 20 \(\mathrm{cm}\), their equivalent power becomes \(+\frac{27}{5} \mathrm{D}\), then their individual powers are

1 \(6 \mathrm{D}\) and \(3 \mathrm{D}\)
2 \(6 \mathrm{D}\) and \(4 \mathrm{D}\)
3 \(9 \mathrm{D}\) and \(3 \mathrm{D}\)
4 \(9 \mathrm{D}\) and \(6 \mathrm{D}\)
Ray Optics

282458 A light beam parallel to axis is incident on the system of four convex lenses \(A, B, C\) and \(D\). Focal lengths of \(A, B, C\) and \(D\) are \(30 \mathrm{~cm}, 10\) \(\mathrm{cm}, 30 \mathrm{~cm}\) and \(10 \mathrm{~cm}\), respectively as shown. Here, fixed distance \(B C=20 \mathrm{~cm}\). What should be the distance between the lens \(A\) and lens \(D\) so that after refractions, rays will be parallel to axis in regions I, III and V?
![original image](https://cdn.mathpix.com/snip/images/DRWKAYScknpSM6uKgx7wRDMGIC_53Fp7NbBd27zcKBs.original.fullsize.png)

1 \(40 \mathrm{~cm}\)
2 \(100 \mathrm{~cm}\)
3 \(80 \mathrm{~cm}\)
4 \(20 \mathrm{~cm}\)
Ray Optics

282459 The distance between a convex lens and a plane mirror is \(10 \mathrm{~cm}\). The parallel rays incident on the convex lens, after reflection from the mirror, form image at the optical centre of the lens. Then the focal length of the lens is

1 \(10 \mathrm{~cm}\)
2 \(20 \mathrm{~cm}\)
3 \(30 \mathrm{~cm}\)
4 \(25 \mathrm{~cm}\)
Ray Optics

282466 The focal length in air of a thin lens made of glass of refractive index 1.5 is \(L\) when immersed in water (refractive index \(=4 / 3\) ), its focal length becomes

1 \(\frac{-\mathrm{L}}{4}\)
2 \(\frac{3 \mathrm{~L}}{4}\)
3 \(4 \mathrm{~L}\)
4 \(\frac{4 \mathrm{~L}}{3}\)
Ray Optics

282457 Two thin lenses have a combined power of +9 D. When they are separated by a distance of 20 \(\mathrm{cm}\), their equivalent power becomes \(+\frac{27}{5} \mathrm{D}\), then their individual powers are

1 \(6 \mathrm{D}\) and \(3 \mathrm{D}\)
2 \(6 \mathrm{D}\) and \(4 \mathrm{D}\)
3 \(9 \mathrm{D}\) and \(3 \mathrm{D}\)
4 \(9 \mathrm{D}\) and \(6 \mathrm{D}\)
Ray Optics

282458 A light beam parallel to axis is incident on the system of four convex lenses \(A, B, C\) and \(D\). Focal lengths of \(A, B, C\) and \(D\) are \(30 \mathrm{~cm}, 10\) \(\mathrm{cm}, 30 \mathrm{~cm}\) and \(10 \mathrm{~cm}\), respectively as shown. Here, fixed distance \(B C=20 \mathrm{~cm}\). What should be the distance between the lens \(A\) and lens \(D\) so that after refractions, rays will be parallel to axis in regions I, III and V?
![original image](https://cdn.mathpix.com/snip/images/DRWKAYScknpSM6uKgx7wRDMGIC_53Fp7NbBd27zcKBs.original.fullsize.png)

1 \(40 \mathrm{~cm}\)
2 \(100 \mathrm{~cm}\)
3 \(80 \mathrm{~cm}\)
4 \(20 \mathrm{~cm}\)
Ray Optics

282459 The distance between a convex lens and a plane mirror is \(10 \mathrm{~cm}\). The parallel rays incident on the convex lens, after reflection from the mirror, form image at the optical centre of the lens. Then the focal length of the lens is

1 \(10 \mathrm{~cm}\)
2 \(20 \mathrm{~cm}\)
3 \(30 \mathrm{~cm}\)
4 \(25 \mathrm{~cm}\)