<p>In this study we investigate the modified transmission eigenvalue problem for spherically symmetric refractive index <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\eta (r)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>η</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. For the direct spectral problem, we prove that the modified transmission eigenvalue problem is equivalent to a Sturm-Liouville problem, and derive asymptotic expressions for the modified eigenvalues. For the inverse spectral problem, we demonstrate that a subsequence of modified transmission eigenvalues corresponding to a parameter sequence with an accumulation point uniquely determines both <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\eta (r)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>η</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and the order <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\( l \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>l</mi> </math></EquationSource> </InlineEquation> of the spherical Bessel function. Furthermore, we provide numerical examples to verify the accuracy of the eigenvalue approximation formulas.</p>