In the following diagram, what is the distance \(x\) if the radius of curvature is \(R= 15​​\text{cm}?\)

    

1. \(30​​\text{cm}\) 2. \(20​​\text{cm}\)
3. \(15​​\text{cm}\) 4. \(10​​\text{cm}\)  
Subtopic:  Refraction at Curved Surface |
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The slab of a refractive index material equal to \(2\) shown in the figure has a curved surface \(APB\) of a radius of curvature of \(10~\text{cm}\) and a plane surface \(CD.\) On the left of \(APB\) is air and on the right of \(CD\) is water with refractive indices as given in the figure. An object \(O\) is placed at a distance of \(15~\text{cm}\) from the pole \(P\) as shown. The distance of the final image of \(O\) from \(P\) as viewed from the left is:
          

1. \(20~\text{cm}\) 2. \(30~\text{cm}\)
3. \(40~\text{cm}\) 4. \(50~\text{cm}\)
Subtopic:  Refraction at Curved Surface |
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A glass sphere \(\left(\mu = \frac{3}{2}\right)\) of radius \(12~\text{cm}\) has a small mark at a distance of \(3~\text{cm}\) from its centre. Where will this mark appear when it is viewed from the side nearest to the mark along the line joining the centre and the mark?
1. \(8~\text{cm}\) inside the sphere 2. \(12~\text{cm}\) inside the sphere
3. \(4~\text{cm}\) inside the sphere 4. \(3~\text{cm}\) inside the sphere
Subtopic:  Refraction at Curved Surface |
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In a glass \((\mu = 1.5)\) sphere with a radius of \(10​​\text{cm},\) there is an air bubble \(B\) at a distance of \(5​​\text{cm}\) from \(C.\) The distance of the bubble from the surface of the sphere (i.e., point \(A\)) as observed from the point \(P\) in the air will be:

            

1. \(4.5​​\text{cm}\) 2. \(20.0​​\text{cm}\)
3. \(9.37​​\text{cm}\) 4. \(6.67​​\text{cm}\)
Subtopic:  Refraction at Curved Surface |
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A mark on the surface of the sphere \(\left(\mu= \frac{3}{2}\right)\) is viewed from a diametrically opposite position. It appears to be at a distance \(15~\text{cm}\) from its actual position. The radius of the sphere is:
1. \(15~\text{cm}\)
2. \(5~\text{cm}\)
3. \(7.5~\text{cm}\) 
4. \(2.5~\text{cm}\)

Subtopic:  Refraction at Curved Surface |
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Level 3: 35%-60%
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