A slanted object AB is placed on one side of convex lens as shown in the diagram. The image is formed on the opposite side. Angle made by the image with principal axis is:

### Related Formula mu = fracsinleft(fracA + delta_m2right)sinleft(fracA2right)$$\mu = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}$$ ### Core Logic Given that the refractive index mu = cotleft(fracA2right)$\mu = \cot\left(\frac{A}{2}\right)$. Substituting this into the prism formula: cotleft(fracA2right) = fracsinleft(fracA + delta_m2right)sinleft(fracA2right)$$\cot\left(\frac{A}{2}\right) = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}$$ fraccosleft(fracA2right)sinleft(fracA2right) = fracsinleft(fracA + delta_m2right)sinleft(fracA2right)$$\frac{\cos\left(\frac{A}{2}\right)}{\sin\left(\frac{A}{2}\right)} = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}$$ Equating the numerators: cosleft(fracA2right) = sinleft(fracA + delta_m2right)$$\cos\left(\frac{A}{2}\right) = \sin\left(\frac{A + \delta_m}{2}\right)$$ We can rewrite cosine in terms of sine: sinleft(fracpi2 - fracA2right) = sinleft(fracA + delta_m2right)$$\sin\left(\frac{\pi}{2} - \frac{A}{2}\right) = \sin\left(\frac{A + \delta_m}{2}\right)$$ ### Step 2: Solve for Deviation Comparing the angles inside the sine functions: fracpi2 - fracA2 = fracA2 + fracdelta_m2$$\frac{\pi}{2} - \frac{A}{2} = \frac{A}{2} + \frac{\delta_m}{2}$$ Multiply the entire equation by 2: pi - A = A + delta_m$$\pi - A = A + \delta_m$$ delta_m = pi - 2A$$\delta_m = \pi - 2A$$ Converting radians to degrees: delta_m = 180^circ - 2A$$\delta_m = 180^{\circ} - 2A$$ ### Pattern Recognition Whenever refractive index mu = cot(A/2)$\mu = \cot(A/2)$, the relation sin(90^circ - A/2)$\sin(90^\circ - A/2)$ strictly matches the prism sine equation, meaning minimum deviation delta_m$\delta_m$ is always 180^circ - 2A$180^\circ - 2A$. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Ray Optics And Optical Instruments