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

282421 Two lenses \(A\) and \(B\) having focal lengths \(2.0 \mathrm{~cm}\) and \(5.0 \mathrm{~cm}\), respectively are placed \(14 \mathrm{~cm}\) apart. Lens \(A\) is placed to the left of lens \(B\). An object is placed \(3 \mathrm{~cm}\) to the left of lens \(A\). The distance of the image from lens \(A\) will be

1 \(\frac{40}{3} \mathrm{~cm}\)
2 \(\frac{82}{3} \mathrm{~cm}\)
3 \(\frac{112}{5} \mathrm{~cm}\)
4 \(\frac{92}{5} \mathrm{~cm}\)
Ray Optics

282422 Three lenses of focal lengths \(+10 \mathrm{~cm},-10 \mathrm{~cm}\) and \(+30 \mathrm{~cm}\) are placed at distance of \(30 \mathrm{~cm}, 35\) \(\mathrm{cm}\) and \(45 \mathrm{~cm}\), respectively from an object. The distance between the object and the image formed is

1 \(100 \mathrm{~cm}\)
2 \(75 \mathrm{~cm}\)
3 \(30 \mathrm{~cm}\)
4 \(45 \mathrm{~cm}\)
Ray Optics

282423 A point object \(O\) is placed on the axis of a cylindrical piece of glass of refractive index 1.6 as shown in the figure. One surface of the glass piece is convex with radius of curvature \(3 \mathrm{~mm}\). The point appeared to be at \(5 \mathrm{~mm}\) on the axis when viewed along the axis and from right side of convex surface. The distance of the point object from the convex surface is :
![original image](https://cdn.mathpix.com/snip/images/rCDoZlnJiSpuZHpWPpqbG1GruOp7GNA9IOx23n09ZI4.original.fullsize.png)

1 \(4 \mathrm{~mm}\)
2 \(6 \mathrm{~mm}\)
3 \(3 \mathrm{~mm}\)
4 \(2.5 \mathrm{~mm}\)
Ray Optics

282424 Where should an object be placed on the axis of a convex lens of focal length \(8 \mathrm{~cm}\), so as to achieve magnification of -4 ? (Distances are measured from optic centre of the lens)

1 \(-6 \mathrm{~cm}\)
2 \(-10 \mathrm{~cm}\)
3 \(-12 \mathrm{~cm}\)
4 \(-9 \mathrm{~cm}\)
Ray Optics

282425 The radii of curvature of the spherical surfaces of a biconvex lens are \(20 \mathrm{~cm}\) and \(30 \mathrm{~cm}\). The refractive index of the material of the lens is 1.65. If the lens is submerged in a liquid of refractive index 1.1, its effective focal length will be

1 \(25 \mathrm{~cm}\)
2 \(30 \mathrm{~cm}\)
3 \(20 \mathrm{~cm}\)
4 \(24 \mathrm{~cm}\)
Ray Optics

282421 Two lenses \(A\) and \(B\) having focal lengths \(2.0 \mathrm{~cm}\) and \(5.0 \mathrm{~cm}\), respectively are placed \(14 \mathrm{~cm}\) apart. Lens \(A\) is placed to the left of lens \(B\). An object is placed \(3 \mathrm{~cm}\) to the left of lens \(A\). The distance of the image from lens \(A\) will be

1 \(\frac{40}{3} \mathrm{~cm}\)
2 \(\frac{82}{3} \mathrm{~cm}\)
3 \(\frac{112}{5} \mathrm{~cm}\)
4 \(\frac{92}{5} \mathrm{~cm}\)
Ray Optics

282422 Three lenses of focal lengths \(+10 \mathrm{~cm},-10 \mathrm{~cm}\) and \(+30 \mathrm{~cm}\) are placed at distance of \(30 \mathrm{~cm}, 35\) \(\mathrm{cm}\) and \(45 \mathrm{~cm}\), respectively from an object. The distance between the object and the image formed is

1 \(100 \mathrm{~cm}\)
2 \(75 \mathrm{~cm}\)
3 \(30 \mathrm{~cm}\)
4 \(45 \mathrm{~cm}\)
Ray Optics

282423 A point object \(O\) is placed on the axis of a cylindrical piece of glass of refractive index 1.6 as shown in the figure. One surface of the glass piece is convex with radius of curvature \(3 \mathrm{~mm}\). The point appeared to be at \(5 \mathrm{~mm}\) on the axis when viewed along the axis and from right side of convex surface. The distance of the point object from the convex surface is :
![original image](https://cdn.mathpix.com/snip/images/rCDoZlnJiSpuZHpWPpqbG1GruOp7GNA9IOx23n09ZI4.original.fullsize.png)

1 \(4 \mathrm{~mm}\)
2 \(6 \mathrm{~mm}\)
3 \(3 \mathrm{~mm}\)
4 \(2.5 \mathrm{~mm}\)
Ray Optics

282424 Where should an object be placed on the axis of a convex lens of focal length \(8 \mathrm{~cm}\), so as to achieve magnification of -4 ? (Distances are measured from optic centre of the lens)

1 \(-6 \mathrm{~cm}\)
2 \(-10 \mathrm{~cm}\)
3 \(-12 \mathrm{~cm}\)
4 \(-9 \mathrm{~cm}\)
Ray Optics

282425 The radii of curvature of the spherical surfaces of a biconvex lens are \(20 \mathrm{~cm}\) and \(30 \mathrm{~cm}\). The refractive index of the material of the lens is 1.65. If the lens is submerged in a liquid of refractive index 1.1, its effective focal length will be

1 \(25 \mathrm{~cm}\)
2 \(30 \mathrm{~cm}\)
3 \(20 \mathrm{~cm}\)
4 \(24 \mathrm{~cm}\)
Ray Optics

282421 Two lenses \(A\) and \(B\) having focal lengths \(2.0 \mathrm{~cm}\) and \(5.0 \mathrm{~cm}\), respectively are placed \(14 \mathrm{~cm}\) apart. Lens \(A\) is placed to the left of lens \(B\). An object is placed \(3 \mathrm{~cm}\) to the left of lens \(A\). The distance of the image from lens \(A\) will be

1 \(\frac{40}{3} \mathrm{~cm}\)
2 \(\frac{82}{3} \mathrm{~cm}\)
3 \(\frac{112}{5} \mathrm{~cm}\)
4 \(\frac{92}{5} \mathrm{~cm}\)
Ray Optics

282422 Three lenses of focal lengths \(+10 \mathrm{~cm},-10 \mathrm{~cm}\) and \(+30 \mathrm{~cm}\) are placed at distance of \(30 \mathrm{~cm}, 35\) \(\mathrm{cm}\) and \(45 \mathrm{~cm}\), respectively from an object. The distance between the object and the image formed is

1 \(100 \mathrm{~cm}\)
2 \(75 \mathrm{~cm}\)
3 \(30 \mathrm{~cm}\)
4 \(45 \mathrm{~cm}\)
Ray Optics

282423 A point object \(O\) is placed on the axis of a cylindrical piece of glass of refractive index 1.6 as shown in the figure. One surface of the glass piece is convex with radius of curvature \(3 \mathrm{~mm}\). The point appeared to be at \(5 \mathrm{~mm}\) on the axis when viewed along the axis and from right side of convex surface. The distance of the point object from the convex surface is :
![original image](https://cdn.mathpix.com/snip/images/rCDoZlnJiSpuZHpWPpqbG1GruOp7GNA9IOx23n09ZI4.original.fullsize.png)

1 \(4 \mathrm{~mm}\)
2 \(6 \mathrm{~mm}\)
3 \(3 \mathrm{~mm}\)
4 \(2.5 \mathrm{~mm}\)
Ray Optics

282424 Where should an object be placed on the axis of a convex lens of focal length \(8 \mathrm{~cm}\), so as to achieve magnification of -4 ? (Distances are measured from optic centre of the lens)

1 \(-6 \mathrm{~cm}\)
2 \(-10 \mathrm{~cm}\)
3 \(-12 \mathrm{~cm}\)
4 \(-9 \mathrm{~cm}\)
Ray Optics

282425 The radii of curvature of the spherical surfaces of a biconvex lens are \(20 \mathrm{~cm}\) and \(30 \mathrm{~cm}\). The refractive index of the material of the lens is 1.65. If the lens is submerged in a liquid of refractive index 1.1, its effective focal length will be

1 \(25 \mathrm{~cm}\)
2 \(30 \mathrm{~cm}\)
3 \(20 \mathrm{~cm}\)
4 \(24 \mathrm{~cm}\)
Ray Optics

282421 Two lenses \(A\) and \(B\) having focal lengths \(2.0 \mathrm{~cm}\) and \(5.0 \mathrm{~cm}\), respectively are placed \(14 \mathrm{~cm}\) apart. Lens \(A\) is placed to the left of lens \(B\). An object is placed \(3 \mathrm{~cm}\) to the left of lens \(A\). The distance of the image from lens \(A\) will be

1 \(\frac{40}{3} \mathrm{~cm}\)
2 \(\frac{82}{3} \mathrm{~cm}\)
3 \(\frac{112}{5} \mathrm{~cm}\)
4 \(\frac{92}{5} \mathrm{~cm}\)
Ray Optics

282422 Three lenses of focal lengths \(+10 \mathrm{~cm},-10 \mathrm{~cm}\) and \(+30 \mathrm{~cm}\) are placed at distance of \(30 \mathrm{~cm}, 35\) \(\mathrm{cm}\) and \(45 \mathrm{~cm}\), respectively from an object. The distance between the object and the image formed is

1 \(100 \mathrm{~cm}\)
2 \(75 \mathrm{~cm}\)
3 \(30 \mathrm{~cm}\)
4 \(45 \mathrm{~cm}\)
Ray Optics

282423 A point object \(O\) is placed on the axis of a cylindrical piece of glass of refractive index 1.6 as shown in the figure. One surface of the glass piece is convex with radius of curvature \(3 \mathrm{~mm}\). The point appeared to be at \(5 \mathrm{~mm}\) on the axis when viewed along the axis and from right side of convex surface. The distance of the point object from the convex surface is :
![original image](https://cdn.mathpix.com/snip/images/rCDoZlnJiSpuZHpWPpqbG1GruOp7GNA9IOx23n09ZI4.original.fullsize.png)

1 \(4 \mathrm{~mm}\)
2 \(6 \mathrm{~mm}\)
3 \(3 \mathrm{~mm}\)
4 \(2.5 \mathrm{~mm}\)
Ray Optics

282424 Where should an object be placed on the axis of a convex lens of focal length \(8 \mathrm{~cm}\), so as to achieve magnification of -4 ? (Distances are measured from optic centre of the lens)

1 \(-6 \mathrm{~cm}\)
2 \(-10 \mathrm{~cm}\)
3 \(-12 \mathrm{~cm}\)
4 \(-9 \mathrm{~cm}\)
Ray Optics

282425 The radii of curvature of the spherical surfaces of a biconvex lens are \(20 \mathrm{~cm}\) and \(30 \mathrm{~cm}\). The refractive index of the material of the lens is 1.65. If the lens is submerged in a liquid of refractive index 1.1, its effective focal length will be

1 \(25 \mathrm{~cm}\)
2 \(30 \mathrm{~cm}\)
3 \(20 \mathrm{~cm}\)
4 \(24 \mathrm{~cm}\)
Ray Optics

282421 Two lenses \(A\) and \(B\) having focal lengths \(2.0 \mathrm{~cm}\) and \(5.0 \mathrm{~cm}\), respectively are placed \(14 \mathrm{~cm}\) apart. Lens \(A\) is placed to the left of lens \(B\). An object is placed \(3 \mathrm{~cm}\) to the left of lens \(A\). The distance of the image from lens \(A\) will be

1 \(\frac{40}{3} \mathrm{~cm}\)
2 \(\frac{82}{3} \mathrm{~cm}\)
3 \(\frac{112}{5} \mathrm{~cm}\)
4 \(\frac{92}{5} \mathrm{~cm}\)
Ray Optics

282422 Three lenses of focal lengths \(+10 \mathrm{~cm},-10 \mathrm{~cm}\) and \(+30 \mathrm{~cm}\) are placed at distance of \(30 \mathrm{~cm}, 35\) \(\mathrm{cm}\) and \(45 \mathrm{~cm}\), respectively from an object. The distance between the object and the image formed is

1 \(100 \mathrm{~cm}\)
2 \(75 \mathrm{~cm}\)
3 \(30 \mathrm{~cm}\)
4 \(45 \mathrm{~cm}\)
Ray Optics

282423 A point object \(O\) is placed on the axis of a cylindrical piece of glass of refractive index 1.6 as shown in the figure. One surface of the glass piece is convex with radius of curvature \(3 \mathrm{~mm}\). The point appeared to be at \(5 \mathrm{~mm}\) on the axis when viewed along the axis and from right side of convex surface. The distance of the point object from the convex surface is :
![original image](https://cdn.mathpix.com/snip/images/rCDoZlnJiSpuZHpWPpqbG1GruOp7GNA9IOx23n09ZI4.original.fullsize.png)

1 \(4 \mathrm{~mm}\)
2 \(6 \mathrm{~mm}\)
3 \(3 \mathrm{~mm}\)
4 \(2.5 \mathrm{~mm}\)
Ray Optics

282424 Where should an object be placed on the axis of a convex lens of focal length \(8 \mathrm{~cm}\), so as to achieve magnification of -4 ? (Distances are measured from optic centre of the lens)

1 \(-6 \mathrm{~cm}\)
2 \(-10 \mathrm{~cm}\)
3 \(-12 \mathrm{~cm}\)
4 \(-9 \mathrm{~cm}\)
Ray Optics

282425 The radii of curvature of the spherical surfaces of a biconvex lens are \(20 \mathrm{~cm}\) and \(30 \mathrm{~cm}\). The refractive index of the material of the lens is 1.65. If the lens is submerged in a liquid of refractive index 1.1, its effective focal length will be

1 \(25 \mathrm{~cm}\)
2 \(30 \mathrm{~cm}\)
3 \(20 \mathrm{~cm}\)
4 \(24 \mathrm{~cm}\)